----------------------------------------------------------------------------------
      name:  <unnamed>
       log:  /Users/thomasjamieson/Dropbox/Academic/Working Papers/Information and
>  Predictions/JEPS_replication.log
  log type:  text
 opened on:  14 Jun 2019, 11:56:24

. do "/Users/thomasjamieson/Dropbox/Academic/Working Papers/Information and Predic
> tions/JEPS_replication.do"

. /***************************************
> Replication Code for "The Effects of Certain and Uncertain Incentives on Effort 
> and Knowledge Accuracy"
> ****************************************/
. 
. clear

. pause on

. set more off

. log on
(log already on)

. use "jeps.dta"

. 
. 
. /***************************************
> Table 1. Descriptive Statistics of Pre-treatment Political Information, by Treat
> ment
> ****************************************/
. 
. /* T-tests for P-Values in Table 1. */
. 
. ttest k_correct if treatment ==0 | treatment ==1, by(treatment_text)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
BonusTre |     256    3.542969    .0822411    1.315857    3.381011    3.704927
ControlC |     256    3.707031    .0884773    1.415637    3.532792    3.881271
---------+--------------------------------------------------------------------
combined |     512       3.625    .0604482    1.367787    3.506242    3.743758
---------+--------------------------------------------------------------------
    diff |           -.1640625    .1207966               -.4013828    .0732578
------------------------------------------------------------------------------
    diff = mean(BonusTre) - mean(ControlC)                        t =  -1.3582
Ho: diff = 0                                     degrees of freedom =      510

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0875         Pr(|T| > |t|) = 0.1750          Pr(T > t) = 0.9125

. ttest k_correct if treatment ==0 | treatment ==2, by(treatment_text)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
ControlC |     256    3.707031    .0884773    1.415637    3.532792    3.881271
RandomBo |     250        3.54    .0874539    1.382768    3.367756    3.712244
---------+--------------------------------------------------------------------
combined |     506    3.624506    .0622645    1.400605    3.502177    3.746835
---------+--------------------------------------------------------------------
    diff |            .1670312     .124439               -.0774519    .4115144
------------------------------------------------------------------------------
    diff = mean(ControlC) - mean(RandomBo)                        t =   1.3423
Ho: diff = 0                                     degrees of freedom =      504

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9099         Pr(|T| > |t|) = 0.1801          Pr(T > t) = 0.0901

. ttest k_correct if treatment ==0 | treatment ==3, by(treatment_text)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
ControlC |     256    3.707031    .0884773    1.415637    3.532792    3.881271
LotteryT |     254    3.531496    .0824872     1.31463    3.369047    3.693945
---------+--------------------------------------------------------------------
combined |     510    3.619608    .0605649    1.367748     3.50062    3.738596
---------+--------------------------------------------------------------------
    diff |            .1755352    .1209995               -.0621859    .4132562
------------------------------------------------------------------------------
    diff = mean(ControlC) - mean(LotteryT)                        t =   1.4507
Ho: diff = 0                                     degrees of freedom =      508

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9263         Pr(|T| > |t|) = 0.1475          Pr(T > t) = 0.0737

. 
. /* Pre-treatment Political Information Questions, By Treatment Group */
. 
. ssc install estout, replace
checking estout consistency and verifying not already installed...

the following files will be replaced:
    /Users/thomasjamieson/Library/Application Support/Stata/ado/plus/e/estpost.ado
    /Users/thomasjamieson/Library/Application Support/Stata/ado/plus/e/estpost.hlp

installing into /Users/thomasjamieson/Library/Application Support/Stata/ado/plus/.
> ..
installation complete.

. 
. estpost tabstat k_correct, by(treatment) stat(count mean sd min max) columns(sta
> t) listwise

Summary statistics: count mean sd min max
     for variables: k_correct
  by categories of: treatment

   treatment |  e(count)    e(mean)      e(sd)     e(min)     e(max) 
-------------+-------------------------------------------------------
           0 |       256   3.707031   1.415637          1          8 
Bonus_Trea~t |       256   3.542969   1.315857          1          7 
Random_Bon~t |       250       3.54   1.382768          1          8 
Lottery_Tr~t |       254   3.531496    1.31463          1          7 
-------------+-------------------------------------------------------
       Total |      1016   3.580709   1.357839          1          8 

. esttab using "table1.tex", cells("count mean(fmt(%4.3f)) sd(fmt(%4.3f)) min max"
> ) replace title({Descriptive Statistics of Pre-treatment Information Accuracy, b
> y Treatment.}\label{tab1})
(output written to table1.tex)

. 
. 
. /***************************************
> Figure 2. Determinants of Effort
> ****************************************/
. 
. ssc install coefplot, replace
checking coefplot consistency and verifying not already installed...
all files already exist and are up to date.

. 
. reg minutes i.treatment, r

Linear regression                               Number of obs     =      1,016
                                                F(3, 1012)        =       2.01
                                                Prob > F          =     0.1106
                                                R-squared         =     0.0052
                                                Root MSE          =     5.8462

---------------------------------------------------------------------------------
                |               Robust
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   1.066406   .4982545     2.14   0.033      .088676    2.044137
Random Bonus..  |   .9808073   .4976482     1.97   0.049     .0042668    1.957348
Lottery Trea..  |   .7826577   .5096066     1.54   0.125    -.2173489    1.782664
                |
          _cons |   10.83086   .3293526    32.89   0.000     10.18457    11.47715
---------------------------------------------------------------------------------

. coefplot, drop(_cons) xline(0, lpattern(dash) lcolor(black)) graphregion(fcolor(
> white)) lcolor(black) msize(small) graphregion(color(white)) mcolor(black) ciopt
> s(lcolor(black)) xlabel(-2(1)2) xscale(range(-2(1)2)) subtitle("Time Spent on Su
> rvey (minutes)", margin(small))

. 
. 
. /***************************************
> Table 3. Descriptive Statistics of Predictive Accuracy, by Treatment.
> ****************************************/
. 
. /* T-tests for P-Values in Table 3. */
. 
. ttest p_correct if treatment ==0 | treatment ==1, by(treatment_text)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
BonusTre |     256    1.171875     .063646    1.018337    1.046536    1.297214
ControlC |     256     .796875    .0555495    .8887919    .6874808    .9062692
---------+--------------------------------------------------------------------
combined |     512     .984375    .0430052     .973097    .8998862    1.068864
---------+--------------------------------------------------------------------
    diff |                .375    .0844782                .2090319    .5409681
------------------------------------------------------------------------------
    diff = mean(BonusTre) - mean(ControlC)                        t =   4.4390
Ho: diff = 0                                     degrees of freedom =      510

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 1.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 0.0000

. ttest p_correct if treatment ==0 | treatment ==2, by(treatment_text)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
ControlC |     256     .796875    .0555495    .8887919    .6874808    .9062692
RandomBo |     250        .964    .0629497    .9953224    .8400182    1.087982
---------+--------------------------------------------------------------------
combined |     506    .8794466    .0420415    .9457003    .7968488    .9620444
---------+--------------------------------------------------------------------
    diff |            -.167125    .0838425               -.3318488   -.0024012
------------------------------------------------------------------------------
    diff = mean(ControlC) - mean(RandomBo)                        t =  -1.9933
Ho: diff = 0                                     degrees of freedom =      504

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0234         Pr(|T| > |t|) = 0.0468          Pr(T > t) = 0.9766

. ttest p_correct if treatment ==0 | treatment ==3, by(treatment_text)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
ControlC |     256     .796875    .0555495    .8887919    .6874808    .9062692
LotteryT |     254    1.090551    .0624868    .9958755    .9674906    1.213612
---------+--------------------------------------------------------------------
combined |     510    .9431373    .0422485     .954105    .8601344     1.02614
---------+--------------------------------------------------------------------
    diff |           -.2936762    .0835711               -.4578637   -.1294887
------------------------------------------------------------------------------
    diff = mean(ControlC) - mean(LotteryT)                        t =  -3.5141
Ho: diff = 0                                     degrees of freedom =      508

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0002         Pr(|T| > |t|) = 0.0005          Pr(T > t) = 0.9998

. 
. /* Pre-treatment Political Information Questions, By Treatment Group */
. 
. estpost tabstat p_correct, by(treatment) stat(count mean sd min max) columns(sta
> t) listwise

Summary statistics: count mean sd min max
     for variables: p_correct
  by categories of: treatment

   treatment |  e(count)    e(mean)      e(sd)     e(min)     e(max) 
-------------+-------------------------------------------------------
           0 |       256    .796875   .8887919          0          5 
Bonus_Trea~t |       256   1.171875   1.018337          0          4 
Random_Bon~t |       250       .964   .9953224          0          5 
Lottery_Tr~t |       254   1.090551   .9958755          0          5 
-------------+-------------------------------------------------------
       Total |      1016   1.005906   .9845929          0          5 

. esttab using "table3.tex", cells("count mean(fmt(%4.3f)) sd(fmt(%4.3f)) min max"
> ) replace title({Descriptive Statistics of Predictive Accuracy, by Treatment.}\l
> abel{tab1})
(output written to table3.tex)

. 
. 
. /***************************************
> Figure 3. Determinants of Knowledge Accuracy
> ****************************************/
. 
. reg p_correct i.treatment, r

Linear regression                               Number of obs     =      1,016
                                                F(3, 1012)        =       7.67
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0208
                                                Root MSE          =     .97573

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |       .375   .0844795     4.44   0.000      .209225     .540775
Random Bonus..  |    .167125   .0839539     1.99   0.047     .0023813    .3318687
Lottery Trea..  |   .2936762   .0836089     3.51   0.000     .1296096    .4577427
                |
          _cons |    .796875   .0555503    14.35   0.000     .6878679    .9058821
---------------------------------------------------------------------------------

. coefplot, drop(_cons) xline(0, lpattern(dash) lcolor(black)) graphregion(fcolor(
> white)) lcolor(black) msize(small) graphregion(color(white)) mcolor(black) ciopt
> s(lcolor(black)) xlabel(-1(0.5)1) xscale(range(-1(0.5)1)) subtitle("Determinants
>  of Knowledge Accuracy", margin(small))

. 
. 
. /***************************************
> Table 4. Direct Treatment Effects and Mediation Effects of Incentives on Knowled
> ge Accuracy
> ****************************************/
. 
. ssc install mediation, replace
checking mediation consistency and verifying not already installed...
all files already exist and are up to date.

. ssc install moremata, replace
checking moremata consistency and verifying not already installed...

the following files will be replaced:
    /Users/thomasjamieson/Library/Application Support/Stata/ado/plus/l/lmoremata.m
> lib
    /Users/thomasjamieson/Library/Application Support/Stata/ado/plus/m/moremata.hl
> p
    /Users/thomasjamieson/Library/Application Support/Stata/ado/plus/m/moremata_so
> urce.hlp

installing into /Users/thomasjamieson/Library/Application Support/Stata/ado/plus/.
> ..
installation complete.

. 
. 
. medeff (regress minutes bonus_treatment k_correct education age income political
> interest newsconsumption vote) (regress p_correct bonus_treatment minutes k_corr
> ect education age income politicalinterest newsconsumption vote), treat(bonus_tr
> eatment) mediate(minutes) sims(1000)
Using 0 and 1 as treatment values

      Source |       SS           df       MS      Number of obs   =       512
-------------+----------------------------------   F(8, 503)       =      4.43
       Model |  1075.80906         8  134.476132   Prob > F        =    0.0000
    Residual |  15275.5081       503  30.3688034   R-squared       =    0.0658
-------------+----------------------------------   Adj R-squared   =    0.0509
       Total |  16351.3172       511  31.9986638   Root MSE        =    5.5108

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
bonus_treatment |   1.082999   .4893716     2.21   0.027     .1215346    2.044463
      k_correct |   .5599648   .1828129     3.06   0.002     .2007939    .9191357
      education |  -.4107057   .1998499    -2.06   0.040    -.8033491   -.0180622
            age |    .087159   .0209852     4.15   0.000     .0459295    .1283886
         income |  -.0077373   .1698052    -0.05   0.964    -.3413522    .3258776
politicalinte~t |  -.1866513   .4418568    -0.42   0.673    -1.054763     .681461
newsconsumption |   -.083935   .4338499    -0.19   0.847    -.9363162    .7684462
           vote |   .0108643   .1310083     0.08   0.934    -.2465266    .2682552
          _cons |   7.344355   1.410474     5.21   0.000     4.573208     10.1155
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       512
-------------+----------------------------------   F(9, 502)       =      7.54
       Model |  57.6089913         9  6.40099904   Prob > F        =    0.0000
    Residual |  426.266009       502  .849135475   R-squared       =    0.1191
-------------+----------------------------------   Adj R-squared   =    0.1033
       Total |     483.875       511  .946917808   Root MSE        =    .92149

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
bonus_treatment |   .3285836   .0822276     4.00   0.000      .167031    .4901362
        minutes |   .0488983   .0074557     6.56   0.000       .03425    .0635465
      k_correct |   .0257206   .0308528     0.83   0.405    -.0348959    .0863371
      education |  -.0022858   .0335579    -0.07   0.946    -.0682169    .0636454
            age |  -.0050617   .0035687    -1.42   0.157    -.0120731    .0019498
         income |   .0089116    .028394     0.31   0.754    -.0468741    .0646974
politicalinte~t |   .0062475   .0738981     0.08   0.933    -.1389401    .1514351
newsconsumption |   .0177631   .0725488     0.24   0.807    -.1247737    .1602998
           vote |    .004957   .0219067     0.23   0.821     -.038083    .0479971
          _cons |   .2781446   .2421252     1.15   0.251     -.197559    .7538482
---------------------------------------------------------------------------------
The number of observations in the data is less than the number of simulations. Exp
> anding the data to the number of simulations
----------------------------------------------------------------------------------
> --
        Effect                 |  Mean           [95% Conf. Interval]
-------------------------------+--------------------------------------------------
> --
        ACME                   |  .0532616      .0047511      .1074927
        Direct Effect          |  .3282976       .168324      .4839642
        Total Effect           |  .3815593      .2246877       .548654
        % of Tot Eff mediated  |  .1389108      .0970769      .2370497
----------------------------------------------------------------------------------
> --

. medeff (regress minutes random_bonus_treatment k_correct education age income po
> liticalinterest newsconsumption vote) (regress p_correct random_bonus_treatment 
> minutes k_correct education age income politicalinterest newsconsumption vote), 
> treat(random_bonus_treatment) mediate(minutes) sims(1000)
Using 0 and 1 as treatment values

      Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(8, 497)       =      3.42
       Model |  829.042594         8  103.630324   Prob > F        =    0.0008
    Residual |  15038.0798       497  30.2577058   R-squared       =    0.0522
-------------+----------------------------------   Adj R-squared   =    0.0370
       Total |  15867.1224       505  31.4200443   Root MSE        =    5.5007

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
random_bonus_~t |   .9667697    .491631     1.97   0.050     .0008383    1.932701
      k_correct |   .3309001   .1796778     1.84   0.066    -.0221215    .6839217
      education |  -.0443541   .1960943    -0.23   0.821    -.4296301    .3409219
            age |   .0835987   .0213371     3.92   0.000     .0416767    .1255207
         income |  -.0268245    .161999    -0.17   0.869    -.3451117    .2914628
politicalinte~t |  -.1866277   .4261002    -0.44   0.662    -1.023807     .650552
newsconsumption |  -.6128047   .4128101    -1.48   0.138    -1.423873    .1982634
           vote |  -.0442688   .1313561    -0.34   0.736    -.3023506    .2138129
          _cons |   8.629887   1.352865     6.38   0.000     5.971848    11.28793
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(9, 496)       =      3.75
       Model |  28.7703252         9   3.1967028   Prob > F        =    0.0001
    Residual |   422.87592       496  .852572419   R-squared       =    0.0637
-------------+----------------------------------   Adj R-squared   =    0.0467
       Total |  451.646245       505     .894349   Root MSE        =    .92335

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
random_bonus_~t |   .1356353   .0828457     1.64   0.102    -.0271364    .2984071
        minutes |   .0352699   .0075296     4.68   0.000     .0204761    .0500636
      k_correct |   .0179504   .0302635     0.59   0.553      -.04151    .0774108
      education |    .027532   .0329181     0.84   0.403    -.0371441    .0922082
            age |  -.0016694   .0036365    -0.46   0.646    -.0088143    .0054755
         income |  -.0056505   .0271939    -0.21   0.835      -.05908     .047779
politicalinte~t |  -.1468532    .071539    -2.05   0.041    -.2874101   -.0062962
newsconsumption |   .1157169   .0694478     1.67   0.096    -.0207312    .2521651
           vote |  -.0252836    .022052    -1.15   0.252    -.0686104    .0180432
          _cons |   .4844804   .2362057     2.05   0.041     .0203934    .9485674
---------------------------------------------------------------------------------
The number of observations in the data is less than the number of simulations. Exp
> anding the data to the number of simulations
----------------------------------------------------------------------------------
> --
        Effect                 |  Mean           [95% Conf. Interval]
-------------------------------+--------------------------------------------------
> --
        ACME                   |  .0343064     -.0008234      .0759402
        Direct Effect          |  .1353472      -.025829       .292184
        Total Effect           |  .1696536      .0125068       .335548
        % of Tot Eff mediated  |  .1978249      .0919209      1.245961
----------------------------------------------------------------------------------
> --

. medeff (regress minutes lottery_treatment k_correct education age income politic
> alinterest newsconsumption vote) (regress p_correct lottery_treatment minutes k_
> correct education age income politicalinterest newsconsumption vote), treat(lott
> ery_treatment) mediate(minutes) sims(1000)
Using 0 and 1 as treatment values

      Source |       SS           df       MS      Number of obs   =       510
-------------+----------------------------------   F(8, 501)       =      2.84
       Model |  732.710853         8  91.5888566   Prob > F        =    0.0043
    Residual |  16144.3655       501  32.2242825   R-squared       =    0.0434
-------------+----------------------------------   Adj R-squared   =    0.0281
       Total |  16877.0764       509   33.157321   Root MSE        =    5.6766

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
lottery_treat~t |   .8347971   .5045131     1.65   0.099     -.156425    1.826019
      k_correct |   .4349527   .1883115     2.31   0.021     .0649752    .8049303
      education |  -.4578621   .2072158    -2.21   0.028    -.8649812    -.050743
            age |   .0542077   .0231654     2.34   0.020     .0086945    .0997209
         income |  -.1707744   .1731921    -0.99   0.325    -.5110467    .1694979
politicalinte~t |   .1449847   .4431302     0.33   0.744    -.7256377    1.015607
newsconsumption |  -.3433065   .4247615    -0.81   0.419     -1.17784    .4912269
           vote |  -.0920151   .1368372    -0.67   0.502    -.3608605    .1768303
          _cons |   9.917222   1.463046     6.78   0.000      7.04276    12.79168
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       510
-------------+----------------------------------   F(9, 500)       =      8.12
       Model |  59.0626776         9  6.56251974   Prob > F        =    0.0000
    Residual |  404.288303       500  .808576606   R-squared       =    0.1275
-------------+----------------------------------   Adj R-squared   =    0.1118
       Total |   463.35098       509  .910316268   Root MSE        =    .89921

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
lottery_treat~t |   .2715092   .0801355     3.39   0.001     .1140655     .428953
        minutes |   .0488209    .007077     6.90   0.000     .0349165    .0627252
      k_correct |   .0686816   .0299879     2.29   0.022     .0097638    .1275994
      education |  -.0116164   .0329836    -0.35   0.725    -.0764199    .0531871
            age |  -.0026235   .0036895    -0.71   0.477    -.0098724    .0046253
         income |   .0075847   .0274611     0.28   0.783    -.0463686    .0615381
politicalinte~t |  -.0963241   .0702015    -1.37   0.171    -.2342505    .0416023
newsconsumption |   .0497423   .0673282     0.74   0.460    -.0825388    .1820234
           vote |  -.0108234   .0216855    -0.50   0.618    -.0534293    .0317825
          _cons |   .2753147   .2421481     1.14   0.256    -.2004384    .7510678
---------------------------------------------------------------------------------
The number of observations in the data is less than the number of simulations. Exp
> anding the data to the number of simulations
----------------------------------------------------------------------------------
> --
        Effect                 |  Mean           [95% Conf. Interval]
-------------------------------+--------------------------------------------------
> --
        ACME                   |  .0411252     -.0085061      .0941393
        Direct Effect          |  .2712305       .115327      .4229366
        Total Effect           |  .3123558      .1570945       .475074
        % of Tot Eff mediated  |  .1308745      .0865662      .2617877
----------------------------------------------------------------------------------
> --

. 
. 
. 
. /***********************************************************
> *** SUPPLEMENTARY MATERIALS ***
> ***********************************************************/
. 
. /***************************************
> Table A1. Descriptive Statistics
> ****************************************/
. 
. estpost summarize p_correct k_correct minutes democrat republican ideology moder
> ate_3 dem_agreement rep_agreement education income male politicalinterest newsco
> nsumption sq_total rel_attendance age white black hisp

             |  e(count)   e(sum_w)    e(mean)     e(Var)      e(sd)     e(min) 
-------------+------------------------------------------------------------------
   p_correct |      1016       1016   1.005906   .9694232   .9845929          0 
   k_correct |      1016       1016   3.580709   1.843726   1.357839          1 
     minutes |      1016       1016   11.53656   34.25575   5.852841        2.3 
    democrat |      1016       1016   .4232283   .2443466   .4943143          0 
  republican |      1016       1016    .265748   .1953183   .4419483          0 
    ideology |      1016       1016   3.591535   3.063534   1.750295          1 
  moderate_3 |      1016       1016   .4744094   .2495908   .4995906          0 
dem_agreem~t |      1016       1016   48.66634   1039.763   32.24536          0 
rep_agreem~t |      1016       1016   36.44685   1051.396   32.42524          0 
   education |      1016       1016   3.308071   1.809432   1.345151          0 
      income |      1016       1016   3.045276     2.4945   1.579399          1 
        male |      1016       1016   .4724409   .2494861   .4994858          0 
politicali~t |      1016       1016   2.404528   1.013536   1.006745          0 
newsconsum~n |      1016       1016   2.429134   1.118126   1.057415          0 
    sq_total |      1016       1016   1.940945   .0556224   .2358439          1 
rel_attend~e |      1016       1016    1.32874   2.492809   1.578863          0 
         age |      1016       1016   39.57677    141.799   11.90794         18 
       white |      1016       1016   .8326772   .1394632   .3734477          0 
       black |      1016       1016   .0954724   .0864425   .2940111          0 
        hisp |      1016       1016   .0501969   .0477241   .2184585          0 

             |    e(max)     e(sum) 
-------------+----------------------
   p_correct |         5       1022 
   k_correct |         8       3638 
     minutes |  47.98333   11721.15 
    democrat |         1        430 
  republican |         1        270 
    ideology |         7       3649 
  moderate_3 |         1        482 
dem_agreem~t |       100      49445 
rep_agreem~t |       100      37030 
   education |         6       3361 
      income |         7       3094 
        male |         1        480 
politicali~t |         4       2443 
newsconsum~n |         4       2468 
    sq_total |         2       1972 
rel_attend~e |         5       1350 
         age |        81      40210 
       white |         1        846 
       black |         1         97 
        hisp |         1         51 

. esttab using "tableA1.tex", cells("count mean sd min max") noobs replace title({
> Descriptive Statistics.}\label{tab1})
(output written to tableA1.tex)

. 
. 
. /***************************************
> Table A2. Descriptive Statistics of Correct Individual Knowledge Questions
> ****************************************/
. 
. estpost summarize p1_correct p2_correct p3_correct p4_correct p5_correct 

             |  e(count)   e(sum_w)    e(mean)     e(Var)      e(sd)     e(min) 
-------------+------------------------------------------------------------------
  p1_correct |      1016       1016   .1240157   .1087429   .3297618          0 
  p2_correct |      1016       1016   .1978346   .1588524    .398563          0 
  p3_correct |      1016       1016   .2057087   .1635536   .4044176          0 
  p4_correct |      1016       1016   .1181102   .1042628   .3228976          0 
  p5_correct |      1016       1016   .3602362   .2306931   .4803053          0 

             |    e(max)     e(sum) 
-------------+----------------------
  p1_correct |         1        126 
  p2_correct |         1        201 
  p3_correct |         1        209 
  p4_correct |         1        120 
  p5_correct |         1        366 

. esttab using "tableA2.tex", cells("count mean sd min max") noobs replace title({
> Descriptive Statistics of Individual Political Prediction Questions.}\label{tab1
> })
(output written to tableA2.tex)

. 
. 
. /*****************************************************
> Table A3. Determinants of Cognitive Effort as Measured by Time Spent (Minutes)
> ******************************************************/
. 
. eststo clear

. 
. /* Column 1 */
. 
. reg minutes i.treatment, r

Linear regression                               Number of obs     =      1,016
                                                F(3, 1012)        =       2.01
                                                Prob > F          =     0.1106
                                                R-squared         =     0.0052
                                                Root MSE          =     5.8462

---------------------------------------------------------------------------------
                |               Robust
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   1.066406   .4982545     2.14   0.033      .088676    2.044137
Random Bonus..  |   .9808073   .4976482     1.97   0.049     .0042668    1.957348
Lottery Trea..  |   .7826577   .5096066     1.54   0.125    -.2173489    1.782664
                |
          _cons |   10.83086   .3293526    32.89   0.000     10.18457    11.47715
---------------------------------------------------------------------------------

. estimates store c1, title(column 1)

. 
. /* Column 2 */
. 
. reg minutes i.treatment democrat republican ideology moderate_3 dem_agreement re
> p_agreement, r

Linear regression                               Number of obs     =      1,016
                                                F(9, 1006)        =       1.69
                                                Prob > F          =     0.0869
                                                R-squared         =     0.0141
                                                Root MSE          =     5.8373

---------------------------------------------------------------------------------
                |               Robust
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   1.083704   .4989781     2.17   0.030      .104547    2.062861
Random Bonus..  |   .9587043   .4982955     1.92   0.055    -.0191134    1.936522
Lottery Trea..  |   .8680856   .5139917     1.69   0.092    -.1405331    1.876704
                |
       democrat |  -1.445892   .5799569    -2.49   0.013    -2.583956    -.307828
     republican |   .0969043   .7470499     0.13   0.897     -1.36905    1.562859
       ideology |   .1850584   .2179363     0.85   0.396    -.2426034    .6127203
     moderate_3 |  -.5014031   .4330793    -1.16   0.247    -1.351245    .3484391
  dem_agreement |   .0219405   .0089065     2.46   0.014     .0044632    .0394179
  rep_agreement |  -.0056522   .0100694    -0.56   0.575    -.0254116    .0141072
          _cons |   10.10824   .9260908    10.91   0.000     8.290946    11.92553
---------------------------------------------------------------------------------

. estimates store c2, title(column 2)

. 
. /* Column 3 */
. 
. reg minutes i.treatment democrat republican ideology moderate_3 dem_agreement re
> p_agreement education income male politicalinterest newsconsumption rel_attendan
> ce age white black hisp, r

Linear regression                               Number of obs     =      1,016
                                                F(19, 996)        =       4.55
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0803
                                                Root MSE          =     5.6662

---------------------------------------------------------------------------------
                |               Robust
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   1.067292   .4815397     2.22   0.027     .1223429     2.01224
Random Bonus..  |   .9140838   .4908317     1.86   0.063    -.0490992    1.877267
Lottery Trea..  |   .8886325   .5097042     1.74   0.082    -.1115849     1.88885
                |
       democrat |  -1.556957    .558477    -2.79   0.005    -2.652884   -.4610307
     republican |   -.037838   .7414774    -0.05   0.959    -1.492875    1.417199
       ideology |    .109726    .217828     0.50   0.615    -.3177285    .5371805
     moderate_3 |  -.5973888   .4260814    -1.40   0.161    -1.433509    .2387316
  dem_agreement |   .0221242   .0088823     2.49   0.013     .0046941    .0395544
  rep_agreement |  -.0052834   .0099642    -0.53   0.596    -.0248366    .0142698
      education |  -.3285164   .1438374    -2.28   0.023    -.6107754   -.0462573
         income |  -.1079205   .1137576    -0.95   0.343    -.3311527    .1153116
           male |  -1.053785   .3629611    -2.90   0.004    -1.766041   -.3415289
politicalinte~t |   .0617256   .3393662     0.18   0.856    -.6042292    .7276805
newsconsumption |  -.2271295   .3252624    -0.70   0.485    -.8654077    .4111486
 rel_attendance |   .1868049   .1311655     1.42   0.155    -.0705874    .4441973
            age |    .097831   .0172431     5.67   0.000      .063994    .1316679
          white |   .0296877   .7003894     0.04   0.966    -1.344721    1.404096
          black |   1.815243   .8085957     2.24   0.025     .2284968     3.40199
           hisp |      1.521   .8892359     1.71   0.087    -.2239907    3.265991
          _cons |   8.416881   1.491711     5.64   0.000     5.489625    11.34414
---------------------------------------------------------------------------------

. estimates store c3, title(column 3)

. 
. /*Building the Table*/
. esttab c1 c2 c3 using "tableA3.tex", b(3) replace unstack nobaselevels label nog
> ap se star (+ 0.1 * 0.05 ** 0.01 *** 0.001) r2 title({Determinants of Informatio
> n Search as Measured by Time Spent (Minutes).}\label{tab1})
(output written to tableA3.tex)

. 
. 
. /*****************************************************
> Table A4. Determinants of Knowledge Accuracy
> ******************************************************/
. 
. eststo clear

. 
. /* Column 1 */
. 
. reg p_correct i.treatment, r

Linear regression                               Number of obs     =      1,016
                                                F(3, 1012)        =       7.67
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0208
                                                Root MSE          =     .97573

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |       .375   .0844795     4.44   0.000      .209225     .540775
Random Bonus..  |    .167125   .0839539     1.99   0.047     .0023813    .3318687
Lottery Trea..  |   .2936762   .0836089     3.51   0.000     .1296096    .4577427
                |
          _cons |    .796875   .0555503    14.35   0.000     .6878679    .9058821
---------------------------------------------------------------------------------

. estimates store c1, title(column 1)

. 
. /* Column 2 */
. 
. reg p_correct i.treatment k_correct democrat republican ideology moderate_3 dem_
> agreement rep_agreement, r

Linear regression                               Number of obs     =      1,016
                                                F(10, 1005)       =       3.09
                                                Prob > F          =     0.0007
                                                R-squared         =     0.0274
                                                Root MSE          =     .97583

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .3839072   .0845406     4.54   0.000     .2180108    .5498035
Random Bonus..  |   .1738253   .0842055     2.06   0.039     .0085864    .3390641
Lottery Trea..  |   .3087776   .0841036     3.67   0.000     .1437389    .4738163
                |
      k_correct |   .0494576   .0235331     2.10   0.036      .003278    .0956372
       democrat |  -.0432971   .0976853    -0.44   0.658    -.2349876    .1483934
     republican |   .0283407   .1087839     0.26   0.795     -.185129    .2418104
       ideology |  -.0315029   .0289834    -1.09   0.277    -.0883777     .025372
     moderate_3 |  -.0393742   .0659024    -0.60   0.550    -.1686963    .0899479
  dem_agreement |  -.0000961   .0015429    -0.06   0.950    -.0031238    .0029317
  rep_agreement |   .0003079   .0016258     0.19   0.850    -.0028825    .0034983
          _cons |   .7481841   .1716749     4.36   0.000     .4113018    1.085066
---------------------------------------------------------------------------------

. estimates store c2, title(column 2)

. 
. /* Column 3 */
. reg p_correct i.treatment k_correct democrat republican ideology moderate_3 dem_
> agreement rep_agreement education income male politicalinterest newsconsumption 
> rel_attendance age white black hisp, r

Linear regression                               Number of obs     =      1,016
                                                F(20, 995)        =       2.40
                                                Prob > F          =     0.0005
                                                R-squared         =     0.0372
                                                Root MSE          =     .97577

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .3926295   .0846736     4.64   0.000     .2264702    .5587889
Random Bonus..  |   .1663792   .0847217     1.96   0.050     .0001254    .3326329
Lottery Trea..  |   .3153757    .083768     3.76   0.000     .1509935    .4797579
                |
      k_correct |   .0583111   .0233521     2.50   0.013     .0124861    .1041361
       democrat |   -.028922   .0978262    -0.30   0.768    -.2208914    .1630475
     republican |   .0016087   .1110493     0.01   0.988    -.2163091    .2195264
       ideology |  -.0338308   .0296971    -1.14   0.255     -.092107    .0244453
     moderate_3 |  -.0477089   .0668623    -0.71   0.476    -.1789162    .0834985
  dem_agreement |   -.000477    .001561    -0.31   0.760    -.0035403    .0025863
  rep_agreement |   .0001058   .0016444     0.06   0.949     -.003121    .0033326
      education |   .0044299   .0247251     0.18   0.858    -.0440894    .0529493
         income |  -.0034644   .0218052    -0.16   0.874    -.0462539    .0393252
           male |  -.1040118   .0627301    -1.66   0.098    -.2271103    .0190867
politicalinte~t |  -.0791464   .0621032    -1.27   0.203    -.2010148    .0427219
newsconsumption |   .0555044   .0585803     0.95   0.344    -.0594508    .1704596
 rel_attendance |    .024242   .0210964     1.15   0.251    -.0171565    .0656406
            age |   .0014207   .0027216     0.52   0.602      -.00392    .0067614
          white |  -.0379829   .1018565    -0.37   0.709    -.2378612    .1618953
          black |  -.1909371   .1292458    -1.48   0.140    -.4445627    .0626885
           hisp |   .0712939   .1444426     0.49   0.622    -.2121531    .3547409
          _cons |   .8120625   .2503776     3.24   0.001     .3207338    1.303391
---------------------------------------------------------------------------------

. estimates store c3, title(column 3)

. 
. /*Building the Table*/
. esttab c1 c2 c3 using "tableA4.tex", b(3) replace unstack nobaselevels label nog
> ap se star (+ 0.1 * 0.05 ** 0.01 *** 0.001) r2 title({Determinants of Knowledge 
> Accuracy.}\label{tab1})
(output written to tableA4.tex)

. 
. 
. /*****************************************************
> Table A5. Determinants of Knowledge Accuracy, including Screening Questions
> ******************************************************/
. 
. eststo clear

. 
. /* Column 1 */
. 
. reg p_correct i.treatment sq_total, r

Linear regression                               Number of obs     =      1,016
                                                F(4, 1011)        =       5.87
                                                Prob > F          =     0.0001
                                                R-squared         =     0.0214
                                                Root MSE          =     .97594

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .3788094   .0847684     4.47   0.000     .2124672    .5451516
Random Bonus..  |   .1684141   .0839813     2.01   0.045     .0036165    .3332117
Lottery Trea..  |   .2917955   .0836447     3.49   0.001     .1276584    .4559325
                |
       sq_total |   .0975206   .1193672     0.82   0.414    -.1367151    .3317564
          _cons |   .6067859   .2381499     2.55   0.011     .1394612    1.074111
---------------------------------------------------------------------------------

. estimates store c1, title(column 1)

. 
. /* Column 2 */
. 
. reg p_correct i.treatment k_correct sq_total democrat republican ideology modera
> te_3 dem_agreement rep_agreement, r

Linear regression                               Number of obs     =      1,016
                                                F(11, 1004)       =       2.86
                                                Prob > F          =     0.0010
                                                R-squared         =     0.0280
                                                Root MSE          =     .97604

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |    .387792   .0848208     4.57   0.000     .2213456    .5542383
Random Bonus..  |   .1750718   .0842675     2.08   0.038     .0097111    .3404325
Lottery Trea..  |   .3070468   .0841428     3.65   0.000     .1419308    .4721627
                |
      k_correct |   .0494403   .0235645     2.10   0.036     .0031989    .0956816
       sq_total |   .0990988   .1185608     0.84   0.403    -.1335567    .3317542
       democrat |  -.0482248   .0981665    -0.49   0.623    -.2408598    .1444102
     republican |   .0307903    .108785     0.28   0.777    -.1826817    .2442623
       ideology |  -.0320191   .0289527    -1.11   0.269    -.0888338    .0247957
     moderate_3 |  -.0380219   .0659614    -0.58   0.564    -.1674599    .0914161
  dem_agreement |  -.0000395    .001546    -0.03   0.980    -.0030734    .0029943
  rep_agreement |   .0003113    .001626     0.19   0.848    -.0028796    .0035021
          _cons |   .5548204   .2890123     1.92   0.055     -.012317    1.121958
---------------------------------------------------------------------------------

. estimates store c2, title(column 2)

. 
. /* Column 3 */
. reg p_correct i.treatment k_correct sq_total democrat republican ideology modera
> te_3 dem_agreement rep_agreement education income male politicalinterest newscon
> sumption rel_attendance age white black hisp, r

Linear regression                               Number of obs     =      1,016
                                                F(21, 994)        =       2.33
                                                Prob > F          =     0.0007
                                                R-squared         =     0.0380
                                                Root MSE          =     .97583

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .3975589   .0849731     4.68   0.000     .2308116    .5643062
Random Bonus..  |   .1681743   .0847829     1.98   0.048     .0018004    .3345483
Lottery Trea..  |   .3133434   .0838063     3.74   0.000     .1488859    .4778009
                |
      k_correct |   .0582721   .0233921     2.49   0.013     .0123685    .1041757
       sq_total |   .1233823   .1186383     1.04   0.299     -.109428    .3561926
       democrat |  -.0344427   .0982904    -0.35   0.726    -.2273233    .1584379
     republican |    .004898   .1111206     0.04   0.965    -.2131599    .2229559
       ideology |  -.0346305   .0296578    -1.17   0.243    -.0928296    .0235685
     moderate_3 |  -.0460163   .0669054    -0.69   0.492    -.1773082    .0852757
  dem_agreement |  -.0004149   .0015636    -0.27   0.791    -.0034832    .0026533
  rep_agreement |   .0001007   .0016428     0.06   0.951    -.0031231    .0033246
      education |    .002968   .0247373     0.12   0.905    -.0455754    .0515113
         income |  -.0035268   .0218397    -0.16   0.872     -.046384    .0393305
           male |  -.1045831   .0627485    -1.67   0.096    -.2277178    .0185515
politicalinte~t |  -.0804137   .0623105    -1.29   0.197    -.2026888    .0418614
newsconsumption |   .0578197   .0588775     0.98   0.326    -.0577189    .1733582
 rel_attendance |   .0249144   .0210979     1.18   0.238    -.0164872    .0663159
            age |   .0015312   .0027286     0.56   0.575    -.0038233    .0068857
          white |  -.0479223   .1021322    -0.47   0.639    -.2483418    .1524973
          black |  -.2006485   .1293486    -1.55   0.121    -.4544762    .0531792
           hisp |   .0632277   .1442168     0.44   0.661    -.2197766     .346232
          _cons |   .5793051   .3352059     1.73   0.084    -.0784874    1.237098
---------------------------------------------------------------------------------

. estimates store c3, title(column 3)

. 
. /*Building the Table*/
. esttab c1 c2 c3 using "tableA5.tex", b(3) replace unstack nobaselevels label nog
> ap se star (+ 0.1 * 0.05 ** 0.01 *** 0.001) r2 title({Determinants of Correct Pr
> edictions, including Screening Questions.}\label{tab1})
(output written to tableA5.tex)

. 
. 
. /*****************************************************
> Table A6. Determinants of Knowledge Accuracy, Pooled Across Treatments
> ******************************************************/
. 
. eststo clear

. 
. /* Column 1 */
. 
. reg p_correct treatment_group, r

Linear regression                               Number of obs     =      1,016
                                                F(1, 1014)        =      17.70
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0152
                                                Root MSE          =     .97756

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
treatment_group |   .2794408   .0664175     4.21   0.000     .1491094    .4097722
          _cons |    .796875   .0554955    14.36   0.000     .6879758    .9057742
---------------------------------------------------------------------------------

. estimates store c1, title(column 1)

. 
. /* Column 2 */
. 
. reg p_correct treatment_group k_correct democrat republican ideology moderate_3 
> dem_agreement rep_agreement, r

Linear regression                               Number of obs     =      1,016
                                                F(8, 1007)        =       3.05
                                                Prob > F          =     0.0022
                                                R-squared         =     0.0216
                                                Root MSE          =     .97775

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
treatment_group |   .2893812   .0666566     4.34   0.000     .1585794     .420183
      k_correct |   .0499442   .0236421     2.11   0.035     .0035508    .0963377
       democrat |  -.0370536   .0969494    -0.38   0.702    -.2272997    .1531924
     republican |   .0208147   .1097215     0.19   0.850    -.1944943    .2361237
       ideology |  -.0317932    .029255    -1.09   0.277    -.0892009    .0256144
     moderate_3 |  -.0396429   .0660382    -0.60   0.548    -.1692312    .0899454
  dem_agreement |  -.0003178   .0015412    -0.21   0.837    -.0033421    .0027065
  rep_agreement |   .0004614   .0016391     0.28   0.778    -.0027551    .0036779
          _cons |   .7523954   .1709515     4.40   0.000     .4169333    1.087857
---------------------------------------------------------------------------------

. estimates store c2, title(column 2)

. 
. /* Column 3 */
. reg p_correct treatment_group k_correct democrat republican ideology moderate_3 
> dem_agreement rep_agreement education income male politicalinterest newsconsumpt
> ion rel_attendance age white black hisp, r

Linear regression                               Number of obs     =      1,016
                                                F(18, 997)        =       2.12
                                                Prob > F          =     0.0041
                                                R-squared         =     0.0305
                                                Root MSE          =     .97816

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
treatment_group |   .2919938   .0664774     4.39   0.000     .1615421    .4224456
      k_correct |   .0577379   .0234608     2.46   0.014     .0116997    .1037761
       democrat |  -.0222625   .0972824    -0.23   0.819    -.2131642    .1686392
     republican |   -.005723   .1116093    -0.05   0.959     -.224739    .2132931
       ideology |  -.0340874   .0299791    -1.14   0.256    -.0929168    .0247419
     moderate_3 |  -.0458357   .0671451    -0.68   0.495    -.1775977    .0859262
  dem_agreement |  -.0007103   .0015577    -0.46   0.649    -.0037671    .0023465
  rep_agreement |   .0002549   .0016578     0.15   0.878    -.0029983    .0035081
      education |   .0038745   .0247071     0.16   0.875    -.0446093    .0523583
         income |  -.0021646   .0217984    -0.10   0.921    -.0449406    .0406113
           male |  -.0972996   .0629237    -1.55   0.122    -.2207776    .0261784
politicalinte~t |  -.0734841   .0620082    -1.19   0.236    -.1951657    .0481975
newsconsumption |   .0551311    .058762     0.94   0.348    -.0601802    .1704425
 rel_attendance |   .0243432   .0209665     1.16   0.246    -.0168004    .0654868
            age |   .0015419   .0027217     0.57   0.571     -.003799    .0068828
          white |  -.0380436   .1034766    -0.37   0.713    -.2411006    .1650133
          black |  -.1835912    .130794    -1.40   0.161    -.4402544     .073072
           hisp |   .0601062   .1450759     0.41   0.679     -.224583    .3447954
          _cons |   .7964702   .2496834     3.19   0.001     .3065049    1.286436
---------------------------------------------------------------------------------

. estimates store c3, title(column 3)

. 
. /*Building the Table*/
. esttab c1 c2 c3 using "tableA6.tex", b(3) replace unstack nobaselevels label nog
> ap se star (+ 0.1 * 0.05 ** 0.01 *** 0.001) r2 title({Determinants of Correct Pr
> edictions, Pooled Across Treatments.}\label{tab1})
(output written to tableA6.tex)

. 
. 
. /*****************************************************
> Table A7. The Effects of Baseline Knowledge on Knowledge Accuracy in Control Gro
> up
> ******************************************************/
. 
. eststo clear

. 
. /* Column 1 */
. 
. reg p_correct k_correct if treatment == 0, r

Linear regression                               Number of obs     =        256
                                                F(1, 254)         =       2.73
                                                Prob > F          =     0.0995
                                                R-squared         =     0.0086
                                                Root MSE          =      .8867

------------------------------------------------------------------------------
             |               Robust
   p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   k_correct |   .0582466   .0352256     1.65   0.099    -.0111249    .1276181
       _cons |   .5809529    .140406     4.14   0.000     .3044446    .8574611
------------------------------------------------------------------------------

. estimates store c1, title(column 1)

. 
. /* Column 2 */
. 
. reg p_correct k_correct democrat republican ideology moderate_3 dem_agreement re
> p_agreement if treatment == 0, r

Linear regression                               Number of obs     =        256
                                                F(7, 248)         =       0.75
                                                Prob > F          =     0.6275
                                                R-squared         =     0.0191
                                                Root MSE          =      .8926

-------------------------------------------------------------------------------
              |               Robust
    p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
    k_correct |   .0570015   .0366943     1.55   0.122    -.0152708    .1292737
     democrat |   .2483444   .1746363     1.42   0.156    -.0956149    .5923037
   republican |  -.0680751   .1654778    -0.41   0.681    -.3939961    .2578459
     ideology |  -.0095584   .0449779    -0.21   0.832    -.0981457    .0790289
   moderate_3 |   .0236031   .1167787     0.20   0.840    -.2064014    .2536075
dem_agreement |  -.0017084    .002527    -0.68   0.500    -.0066854    .0032687
rep_agreement |   .0024852   .0024931     1.00   0.320    -.0024252    .0073956
        _cons |   .5160432   .2832433     1.82   0.070    -.0418258    1.073912
-------------------------------------------------------------------------------

. estimates store c2, title(column 2)

. 
. /* Column 3 */
. reg p_correct k_correct democrat republican ideology moderate_3 dem_agreement re
> p_agreement education income male politicalinterest newsconsumption rel_attendan
> ce age white black hisp if treatment == 0, r

Linear regression                               Number of obs     =        256
                                                F(17, 238)        =       1.10
                                                Prob > F          =     0.3585
                                                R-squared         =     0.0604
                                                Root MSE          =     .89175

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      k_correct |    .073359   .0359539     2.04   0.042     .0025304    .1441877
       democrat |   .2248716   .1715641     1.31   0.191    -.1131066    .5628498
     republican |  -.0818551   .1832863    -0.45   0.656    -.4429256    .2792155
       ideology |  -.0140392   .0470783    -0.30   0.766    -.1067827    .0787042
     moderate_3 |  -.0192801   .1221808    -0.16   0.875     -.259974    .2214138
  dem_agreement |  -.0018838   .0025698    -0.73   0.464    -.0069463    .0031787
  rep_agreement |    .001768   .0026048     0.68   0.498    -.0033634    .0068994
      education |  -.0334616   .0465569    -0.72   0.473    -.1251778    .0582546
         income |   .0024094    .044082     0.05   0.956    -.0844313    .0892501
           male |  -.0831182   .1253786    -0.66   0.508    -.3301117    .1638753
politicalinte~t |  -.0777081   .0983417    -0.79   0.430    -.2714395    .1160233
newsconsumption |   .0433611   .0951802     0.46   0.649     -.144142    .2308643
 rel_attendance |   .0280821   .0361334     0.78   0.438       -.0431    .0992642
            age |  -.0010302   .0049344    -0.21   0.835    -.0107509    .0086905
          white |  -.1101515   .2119886    -0.52   0.604    -.5277652    .3074622
          black |  -.3812776   .2414572    -1.58   0.116    -.8569439    .0943887
           hisp |   .4037111   .2809702     1.44   0.152     -.149795    .9572173
          _cons |   .8687657   .3985433     2.18   0.030     .0836428    1.653889
---------------------------------------------------------------------------------

. estimates store c3, title(column 3)

. 
. /*Building the Table*/
. esttab c1 c2 c3 using "tableA7.tex", b(3) replace unstack nobaselevels label nog
> ap se star (+ 0.1 * 0.05 ** 0.01 *** 0.001) r2 title({The Effects of Knowledge o
> n Correct Predictions in Control Group.}\label{tab1})
(output written to tableA7.tex)

. 
. 
. /*****************************************************
> Table A8. Determinants of Correct Individual Knowledge Questions (Logit)
> ******************************************************/
. 
. eststo clear

. 
. /* Column 1 */
. 
. logit p1_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -380.84806  
Iteration 1:   log pseudolikelihood = -376.62451  
Iteration 2:   log pseudolikelihood = -376.56528  
Iteration 3:   log pseudolikelihood = -376.56526  

Logistic regression                             Number of obs     =      1,016
                                                Wald chi2(3)      =       8.44
                                                Prob > chi2       =     0.0377
Log pseudolikelihood = -376.56526               Pseudo R2         =     0.0112

---------------------------------------------------------------------------------
                |               Robust
     p1_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .4585748   .2799596     1.64   0.101    -.0901359    1.007286
Random Bonus..  |   .0262023   .3035773     0.09   0.931    -.5687982    .6212028
Lottery Trea..  |   .6497669   .2730877     2.38   0.017     .1145248    1.185009
                |
          _cons |  -2.268683   .2145281   -10.58   0.000    -2.689151   -1.848216
---------------------------------------------------------------------------------

. estimates store c1, title(column 1)

. 
. /* Column 2 */
. 
. logit p2_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -505.34409  
Iteration 1:   log pseudolikelihood =  -502.1656  
Iteration 2:   log pseudolikelihood = -502.14558  
Iteration 3:   log pseudolikelihood = -502.14558  

Logistic regression                             Number of obs     =      1,016
                                                Wald chi2(3)      =       6.32
                                                Prob > chi2       =     0.0970
Log pseudolikelihood = -502.14558               Pseudo R2         =     0.0063

---------------------------------------------------------------------------------
                |               Robust
     p2_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .5456752   .2257509     2.42   0.016     .1032116    .9881388
Random Bonus..  |   .3493756   .2323016     1.50   0.133    -.1059271    .8046783
Lottery Trea..  |   .2038277   .2362034     0.86   0.388    -.2591225    .6667779
                |
          _cons |  -1.686399   .1722174    -9.79   0.000    -2.023939   -1.348859
---------------------------------------------------------------------------------

. estimates store c2, title(column 2)

. 
. /* Column 3 */
. 
. logit p3_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -516.34663  
Iteration 1:   log pseudolikelihood = -513.15525  
Iteration 2:   log pseudolikelihood = -513.13133  
Iteration 3:   log pseudolikelihood = -513.13132  

Logistic regression                             Number of obs     =      1,016
                                                Wald chi2(3)      =       6.06
                                                Prob > chi2       =     0.1089
Log pseudolikelihood = -513.13132               Pseudo R2         =     0.0062

---------------------------------------------------------------------------------
                |               Robust
     p3_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |     .44337   .2305619     1.92   0.054     -.008523     .895263
Random Bonus..  |   .4506693   .2315429     1.95   0.052    -.0031464    .9044851
Lottery Trea..  |   .5208736   .2288629     2.28   0.023     .0723105    .9694367
                |
          _cons |  -1.716336    .174009    -9.86   0.000    -2.057387   -1.375284
---------------------------------------------------------------------------------

. estimates store c3, title(column 3)

. 
. /* Column 4 */
. 
. logit p4_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -368.95307  
Iteration 1:   log pseudolikelihood = -364.28509  
Iteration 2:   log pseudolikelihood = -364.18926  
Iteration 3:   log pseudolikelihood =  -364.1892  
Iteration 4:   log pseudolikelihood =  -364.1892  

Logistic regression                             Number of obs     =      1,016
                                                Wald chi2(3)      =       9.17
                                                Prob > chi2       =     0.0271
Log pseudolikelihood =  -364.1892               Pseudo R2         =     0.0129

---------------------------------------------------------------------------------
                |               Robust
     p4_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .2881168   .3116765     0.92   0.355     -.322758    .8989916
Random Bonus..  |   .8098715   .2899689     2.79   0.005     .2415429      1.3782
Lottery Trea..  |   .6008325   .2971219     2.02   0.043     .0184844    1.183181
                |
          _cons |    -2.4681   .2330037   -10.59   0.000    -2.924778   -2.011421
---------------------------------------------------------------------------------

. estimates store c4, title(column 4)

. 
. /* Column 5 */
. 
. logit p5_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -664.01085  
Iteration 1:   log pseudolikelihood = -652.89814  
Iteration 2:   log pseudolikelihood = -652.87001  
Iteration 3:   log pseudolikelihood = -652.87001  

Logistic regression                             Number of obs     =      1,016
                                                Wald chi2(3)      =      22.05
                                                Prob > chi2       =     0.0001
Log pseudolikelihood = -652.87001               Pseudo R2         =     0.0168

---------------------------------------------------------------------------------
                |               Robust
     p5_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .6451737    .183792     3.51   0.000      .284948    1.005399
Random Bonus..  |  -.1741248   .1947783    -0.89   0.371    -.5558832    .2076336
Lottery Trea..  |   .2553095    .186842     1.37   0.172    -.1108942    .6215132
                |
          _cons |  -.7703368   .1344536    -5.73   0.000    -1.033861   -.5068127
---------------------------------------------------------------------------------

. estimates store c5, title(column 5)

. 
. /*Building the Figure*/
. esttab c1 c2 c3 c4 c5 using "tableA8.tex", b(3) replace unstack nobaselevels lab
> el nogap se star (+ 0.1 * 0.05 ** 0.01 *** 0.001) pr2 title({Determinants of Cor
> rect Individual Predictions (Logit).}\label{tab1})
(output written to tableA8.tex)

. 
. 
. /*****************************************************
> Table A9. Randomization Check: F-test of Joint Orthogonality
> ******************************************************/
. 
. ssc install orth_out, replace
checking orth_out consistency and verifying not already installed...
all files already exist and are up to date.

. 
. orth_out democrat republican ideology moderate_3 dem_agreement rep_agreement edu
> cation income male politicalinterest newsconsumption rel_attendance age white bl
> ack hisp using "tableA9.tex", by(treatment) se test latex replace

                                       0:  Bonus Tre~t:  Random Bo~t:
                                       _             _             _
             Democrat:mean         0.430         0.367         0.436
                        se         0.031         0.030         0.031
           Republican:mean         0.270         0.273         0.236
                        se         0.028         0.028         0.027
   Political Ideology:mean         3.555         3.703         3.432
                        se         0.113         0.107         0.110
             Moderate:mean         0.457         0.469         0.460
                        se         0.031         0.031         0.032
Dem. Policy Agreement:mean        49.793        44.758        51.824
                        se         2.041         2.008         2.031
Rep. Policy Agreement:mean        35.980        39.371        33.484
                        se         2.078         2.039         1.971
            Education:mean         3.363         3.254         3.256
                        se         0.085         0.083         0.085
               Income:mean         3.125         3.027         2.920
                        se         0.098         0.098         0.103
                 Male:mean         0.484         0.516         0.432
                        se         0.031         0.031         0.031
   Political interest:mean         2.426         2.480         2.288
                        se         0.063         0.062         0.067
     News Consumption:mean         2.469         2.488         2.324
                        se         0.063         0.064         0.072
 Religious Attendance:mean         1.355         1.363         1.296
                        se         0.100         0.100         0.098
                  Age:mean        39.516        39.973        38.912
                        se         0.742         0.774         0.781
                White:mean         0.801         0.844         0.840
                        se         0.025         0.023         0.023
     African-American:mean         0.102         0.094         0.084
                        se         0.019         0.018         0.018
      Hispanic/Latino:mean         0.066         0.051         0.064
                        se         0.016         0.014         0.016

                             Lottery T~t:  p-value f~y:
                                       _             _
             Democrat:mean         0.461         0.175
                        se         0.031             .
           Republican:mean         0.283         0.652
                        se         0.028             .
   Political Ideology:mean         3.673         0.286
                        se         0.109             .
             Moderate:mean         0.512         0.578
                        se         0.031             .
Dem. Policy Agreement:mean        48.362         0.090
                        se         1.999             .
Rep. Policy Agreement:mean        36.886         0.234
                        se         2.041             .
            Education:mean         3.358         0.666
                        se         0.085             .
               Income:mean         3.106         0.452
                        se         0.098             .
                 Male:mean         0.457         0.267
                        se         0.031             .
   Political interest:mean         2.421         0.173
                        se         0.061             .
     News Consumption:mean         2.433         0.304
                        se         0.066             .
 Religious Attendance:mean         1.299         0.942
                        se         0.098             .
                  Age:mean        39.894         0.742
                        se         0.692             .
                White:mean         0.846         0.470
                        se         0.023             .
     African-American:mean         0.102         0.888
                        se         0.019             .
      Hispanic/Latino:mean         0.020         0.061
                        se         0.009             .

. 
. 
. /*****************************************************
> Table A10. Randomization Check: F-test of Joint Orthogonality
> ******************************************************/
. 
. orth_out democrat republican ideology moderate_3 dem_agreement rep_agreement edu
> cation income male politicalinterest newsconsumption rel_attendance age white bl
> ack hisp using "tableA10.tex", by(treatment) test pcompare count latex replace

                                       0:  Bonus Tre~t:  Random Bo~t:
                                       _             _             _
             Democrat:mean         0.430         0.367         0.436
           Republican:mean         0.270         0.273         0.236
   Political Ideology:mean         3.555         3.703         3.432
             Moderate:mean         0.457         0.469         0.460
Dem. Policy Agreement:mean        49.793        44.758        51.824
Rep. Policy Agreement:mean        35.980        39.371        33.484
            Education:mean         3.363         3.254         3.256
               Income:mean         3.125         3.027         2.920
                 Male:mean         0.484         0.516         0.432
   Political interest:mean         2.426         2.480         2.288
     News Consumption:mean         2.469         2.488         2.324
 Religious Attendance:mean         1.355         1.363         1.296
                  Age:mean        39.516        39.973        38.912
                White:mean         0.801         0.844         0.840
     African-American:mean         0.102         0.094         0.084
      Hispanic/Latino:mean         0.066         0.051         0.064
                       N:_       256.000       256.000       250.000

                             Lottery T~t:  (1) vs. (~e:  (1) vs. (~e:
                                       _             _             _
             Democrat:mean         0.461         0.149         0.886
           Republican:mean         0.283         0.921         0.387
   Political Ideology:mean         3.673         0.341         0.437
             Moderate:mean         0.512         0.791         0.947
Dem. Policy Agreement:mean        48.362         0.079         0.481
Rep. Policy Agreement:mean        36.886         0.245         0.384
            Education:mean         3.358         0.358         0.372
               Income:mean         3.106         0.479         0.149
                 Male:mean         0.457         0.480         0.238
   Political interest:mean         2.421         0.536         0.134
     News Consumption:mean         2.433         0.828         0.132
 Religious Attendance:mean         1.299         0.956         0.672
                  Age:mean        39.894         0.670         0.575
                White:mean         0.846         0.204         0.252
     African-American:mean         0.102         0.766         0.497
      Hispanic/Latino:mean         0.020         0.453         0.913
                       N:_       254.000             .             .

                             (1) vs. (~e:  (2) vs. (~e:  (2) vs. (~e:
                                       _             _             _
             Democrat:mean         0.483         0.115         0.032
           Republican:mean         0.726         0.335         0.801
   Political Ideology:mean         0.452         0.077         0.845
             Moderate:mean         0.217         0.844         0.332
Dem. Policy Agreement:mean         0.617         0.014         0.204
Rep. Policy Agreement:mean         0.756         0.038         0.389
            Education:mean         0.967         0.986         0.380
               Income:mean         0.893         0.450         0.569
                 Male:mean         0.532         0.060         0.184
   Political interest:mean         0.959         0.035         0.495
     News Consumption:mean         0.696         0.089         0.547
 Religious Attendance:mean         0.689         0.631         0.648
                  Age:mean         0.710         0.335         0.939
                White:mean         0.177         0.908         0.933
     African-American:mean         0.976         0.701         0.744
      Hispanic/Latino:mean         0.009         0.523         0.057
                       N:_             .             .             .

                             (3) vs. (~e:  p-value f~y:
                                       _             _
             Democrat:mean         0.579         0.175
           Republican:mean         0.225         0.652
   Political Ideology:mean         0.119         0.286
             Moderate:mean         0.245         0.578
Dem. Policy Agreement:mean         0.225         0.090
Rep. Policy Agreement:mean         0.231         0.234
            Education:mean         0.395         0.666
               Income:mean         0.191         0.452
                 Male:mean         0.578         0.267
   Political interest:mean         0.140         0.173
     News Consumption:mean         0.265         0.304
 Religious Attendance:mean         0.982         0.942
                  Age:mean         0.347         0.742
                White:mean         0.842         0.470
     African-American:mean         0.479         0.888
      Hispanic/Latino:mean         0.013         0.061
                       N:_             .             .

. 
. 
. /*****************************************************
> Table A11. Direct Treatment Effects and Mediation Effects of Incentives on Knowl
> edge Accuracy
> ******************************************************/
. 
. medeff (regress minutes bonus_treatment k_correct education age income political
> interest newsconsumption vote) (regress p_correct bonus_treatment minutes k_corr
> ect education age income politicalinterest newsconsumption vote), treat(bonus_tr
> eatment) mediate(minutes) sims(1000)
Using 0 and 1 as treatment values

      Source |       SS           df       MS      Number of obs   =       512
-------------+----------------------------------   F(8, 503)       =      4.43
       Model |  1075.80906         8  134.476132   Prob > F        =    0.0000
    Residual |  15275.5081       503  30.3688034   R-squared       =    0.0658
-------------+----------------------------------   Adj R-squared   =    0.0509
       Total |  16351.3172       511  31.9986638   Root MSE        =    5.5108

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
bonus_treatment |   1.082999   .4893716     2.21   0.027     .1215346    2.044463
      k_correct |   .5599648   .1828129     3.06   0.002     .2007939    .9191357
      education |  -.4107057   .1998499    -2.06   0.040    -.8033491   -.0180622
            age |    .087159   .0209852     4.15   0.000     .0459295    .1283886
         income |  -.0077373   .1698052    -0.05   0.964    -.3413522    .3258776
politicalinte~t |  -.1866513   .4418568    -0.42   0.673    -1.054763     .681461
newsconsumption |   -.083935   .4338499    -0.19   0.847    -.9363162    .7684462
           vote |   .0108643   .1310083     0.08   0.934    -.2465266    .2682552
          _cons |   7.344355   1.410474     5.21   0.000     4.573208     10.1155
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       512
-------------+----------------------------------   F(9, 502)       =      7.54
       Model |  57.6089913         9  6.40099904   Prob > F        =    0.0000
    Residual |  426.266009       502  .849135475   R-squared       =    0.1191
-------------+----------------------------------   Adj R-squared   =    0.1033
       Total |     483.875       511  .946917808   Root MSE        =    .92149

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
bonus_treatment |   .3285836   .0822276     4.00   0.000      .167031    .4901362
        minutes |   .0488983   .0074557     6.56   0.000       .03425    .0635465
      k_correct |   .0257206   .0308528     0.83   0.405    -.0348959    .0863371
      education |  -.0022858   .0335579    -0.07   0.946    -.0682169    .0636454
            age |  -.0050617   .0035687    -1.42   0.157    -.0120731    .0019498
         income |   .0089116    .028394     0.31   0.754    -.0468741    .0646974
politicalinte~t |   .0062475   .0738981     0.08   0.933    -.1389401    .1514351
newsconsumption |   .0177631   .0725488     0.24   0.807    -.1247737    .1602998
           vote |    .004957   .0219067     0.23   0.821     -.038083    .0479971
          _cons |   .2781446   .2421252     1.15   0.251     -.197559    .7538482
---------------------------------------------------------------------------------
The number of observations in the data is less than the number of simulations. Exp
> anding the data to the number of simulations
----------------------------------------------------------------------------------
> --
        Effect                 |  Mean           [95% Conf. Interval]
-------------------------------+--------------------------------------------------
> --
        ACME                   |  .0532616      .0047511      .1074927
        Direct Effect          |  .3282976       .168324      .4839642
        Total Effect           |  .3815593      .2246877       .548654
        % of Tot Eff mediated  |  .1389108      .0970769      .2370497
----------------------------------------------------------------------------------
> --

. medeff (regress minutes random_bonus_treatment k_correct education age income po
> liticalinterest newsconsumption vote) (regress p_correct random_bonus_treatment 
> minutes k_correct education age income politicalinterest newsconsumption vote), 
> treat(random_bonus_treatment) mediate(minutes) sims(1000)
Using 0 and 1 as treatment values

      Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(8, 497)       =      3.42
       Model |  829.042594         8  103.630324   Prob > F        =    0.0008
    Residual |  15038.0798       497  30.2577058   R-squared       =    0.0522
-------------+----------------------------------   Adj R-squared   =    0.0370
       Total |  15867.1224       505  31.4200443   Root MSE        =    5.5007

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
random_bonus_~t |   .9667697    .491631     1.97   0.050     .0008383    1.932701
      k_correct |   .3309001   .1796778     1.84   0.066    -.0221215    .6839217
      education |  -.0443541   .1960943    -0.23   0.821    -.4296301    .3409219
            age |   .0835987   .0213371     3.92   0.000     .0416767    .1255207
         income |  -.0268245    .161999    -0.17   0.869    -.3451117    .2914628
politicalinte~t |  -.1866277   .4261002    -0.44   0.662    -1.023807     .650552
newsconsumption |  -.6128047   .4128101    -1.48   0.138    -1.423873    .1982634
           vote |  -.0442688   .1313561    -0.34   0.736    -.3023506    .2138129
          _cons |   8.629887   1.352865     6.38   0.000     5.971848    11.28793
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(9, 496)       =      3.75
       Model |  28.7703252         9   3.1967028   Prob > F        =    0.0001
    Residual |   422.87592       496  .852572419   R-squared       =    0.0637
-------------+----------------------------------   Adj R-squared   =    0.0467
       Total |  451.646245       505     .894349   Root MSE        =    .92335

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
random_bonus_~t |   .1356353   .0828457     1.64   0.102    -.0271364    .2984071
        minutes |   .0352699   .0075296     4.68   0.000     .0204761    .0500636
      k_correct |   .0179504   .0302635     0.59   0.553      -.04151    .0774108
      education |    .027532   .0329181     0.84   0.403    -.0371441    .0922082
            age |  -.0016694   .0036365    -0.46   0.646    -.0088143    .0054755
         income |  -.0056505   .0271939    -0.21   0.835      -.05908     .047779
politicalinte~t |  -.1468532    .071539    -2.05   0.041    -.2874101   -.0062962
newsconsumption |   .1157169   .0694478     1.67   0.096    -.0207312    .2521651
           vote |  -.0252836    .022052    -1.15   0.252    -.0686104    .0180432
          _cons |   .4844804   .2362057     2.05   0.041     .0203934    .9485674
---------------------------------------------------------------------------------
The number of observations in the data is less than the number of simulations. Exp
> anding the data to the number of simulations
----------------------------------------------------------------------------------
> --
        Effect                 |  Mean           [95% Conf. Interval]
-------------------------------+--------------------------------------------------
> --
        ACME                   |  .0343064     -.0008234      .0759402
        Direct Effect          |  .1353472      -.025829       .292184
        Total Effect           |  .1696536      .0125068       .335548
        % of Tot Eff mediated  |  .1978249      .0919209      1.245961
----------------------------------------------------------------------------------
> --

. medeff (regress minutes lottery_treatment k_correct education age income politic
> alinterest newsconsumption vote) (regress p_correct lottery_treatment minutes k_
> correct education age income politicalinterest newsconsumption vote), treat(lott
> ery_treatment) mediate(minutes) sims(1000)
Using 0 and 1 as treatment values

      Source |       SS           df       MS      Number of obs   =       510
-------------+----------------------------------   F(8, 501)       =      2.84
       Model |  732.710853         8  91.5888566   Prob > F        =    0.0043
    Residual |  16144.3655       501  32.2242825   R-squared       =    0.0434
-------------+----------------------------------   Adj R-squared   =    0.0281
       Total |  16877.0764       509   33.157321   Root MSE        =    5.6766

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
lottery_treat~t |   .8347971   .5045131     1.65   0.099     -.156425    1.826019
      k_correct |   .4349527   .1883115     2.31   0.021     .0649752    .8049303
      education |  -.4578621   .2072158    -2.21   0.028    -.8649812    -.050743
            age |   .0542077   .0231654     2.34   0.020     .0086945    .0997209
         income |  -.1707744   .1731921    -0.99   0.325    -.5110467    .1694979
politicalinte~t |   .1449847   .4431302     0.33   0.744    -.7256377    1.015607
newsconsumption |  -.3433065   .4247615    -0.81   0.419     -1.17784    .4912269
           vote |  -.0920151   .1368372    -0.67   0.502    -.3608605    .1768303
          _cons |   9.917222   1.463046     6.78   0.000      7.04276    12.79168
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       510
-------------+----------------------------------   F(9, 500)       =      8.12
       Model |  59.0626776         9  6.56251974   Prob > F        =    0.0000
    Residual |  404.288303       500  .808576606   R-squared       =    0.1275
-------------+----------------------------------   Adj R-squared   =    0.1118
       Total |   463.35098       509  .910316268   Root MSE        =    .89921

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
lottery_treat~t |   .2715092   .0801355     3.39   0.001     .1140655     .428953
        minutes |   .0488209    .007077     6.90   0.000     .0349165    .0627252
      k_correct |   .0686816   .0299879     2.29   0.022     .0097638    .1275994
      education |  -.0116164   .0329836    -0.35   0.725    -.0764199    .0531871
            age |  -.0026235   .0036895    -0.71   0.477    -.0098724    .0046253
         income |   .0075847   .0274611     0.28   0.783    -.0463686    .0615381
politicalinte~t |  -.0963241   .0702015    -1.37   0.171    -.2342505    .0416023
newsconsumption |   .0497423   .0673282     0.74   0.460    -.0825388    .1820234
           vote |  -.0108234   .0216855    -0.50   0.618    -.0534293    .0317825
          _cons |   .2753147   .2421481     1.14   0.256    -.2004384    .7510678
---------------------------------------------------------------------------------
The number of observations in the data is less than the number of simulations. Exp
> anding the data to the number of simulations
----------------------------------------------------------------------------------
> --
        Effect                 |  Mean           [95% Conf. Interval]
-------------------------------+--------------------------------------------------
> --
        ACME                   |  .0411252     -.0085061      .0941393
        Direct Effect          |  .2712305       .115327      .4229366
        Total Effect           |  .3123558      .1570945       .475074
        % of Tot Eff mediated  |  .1308745      .0865662      .2617877
----------------------------------------------------------------------------------
> --

. 
. 
. /*****************************************************
> Figure A2. Average Causal Mediation Effect of the Bonus Treatment on Knowledge A
> ccuracy as a Function Degree of Violation of Sequential Ignorability Assumption.
> ******************************************************/
. 
. medsens (regress minutes bonus_treatment k_correct education age income politica
> linterest newsconsumption vote) (regress p_correct bonus_treatment minutes k_cor
> rect education age income politicalinterest newsconsumption vote), treat(bonus_t
> reatment) mediate(minutes) sims(1000)
Dropping existing variable _med_rho
Dropping existing variable _med_delta0
Dropping existing variable _med_updelta0
Dropping existing variable _med_lodelta0
Dropping existing variable _med_delta1
Dropping existing variable _med_updelta1
Dropping existing variable _med_lodelta1

      Source |       SS           df       MS      Number of obs   =       512
-------------+----------------------------------   F(8, 503)       =      4.43
       Model |  1075.80906         8  134.476132   Prob > F        =    0.0000
    Residual |  15275.5081       503  30.3688034   R-squared       =    0.0658
-------------+----------------------------------   Adj R-squared   =    0.0509
       Total |  16351.3172       511  31.9986638   Root MSE        =    5.5108

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
bonus_treatment |   1.082999   .4893716     2.21   0.027     .1215346    2.044463
      k_correct |   .5599648   .1828129     3.06   0.002     .2007939    .9191357
      education |  -.4107057   .1998499    -2.06   0.040    -.8033491   -.0180622
            age |    .087159   .0209852     4.15   0.000     .0459295    .1283886
         income |  -.0077373   .1698052    -0.05   0.964    -.3413522    .3258776
politicalinte~t |  -.1866513   .4418568    -0.42   0.673    -1.054763     .681461
newsconsumption |   -.083935   .4338499    -0.19   0.847    -.9363162    .7684462
           vote |   .0108643   .1310083     0.08   0.934    -.2465266    .2682552
          _cons |   7.344355   1.410474     5.21   0.000     4.573208     10.1155
---------------------------------------------------------------------------------
(504 missing values generated)

      Source |       SS           df       MS      Number of obs   =       512
-------------+----------------------------------   F(9, 502)       =      7.54
       Model |  57.6089913         9  6.40099904   Prob > F        =    0.0000
    Residual |  426.266009       502  .849135475   R-squared       =    0.1191
-------------+----------------------------------   Adj R-squared   =    0.1033
       Total |     483.875       511  .946917808   Root MSE        =    .92149

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        minutes |   .0488983   .0074557     6.56   0.000       .03425    .0635465
bonus_treatment |   .3285836   .0822276     4.00   0.000      .167031    .4901362
      k_correct |   .0257206   .0308528     0.83   0.405    -.0348959    .0863371
      education |  -.0022858   .0335579    -0.07   0.946    -.0682169    .0636454
            age |  -.0050617   .0035687    -1.42   0.157    -.0120731    .0019498
         income |   .0089116    .028394     0.31   0.754    -.0468741    .0646974
politicalinte~t |   .0062475   .0738981     0.08   0.933    -.1389401    .1514351
newsconsumption |   .0177631   .0725488     0.24   0.807    -.1247737    .1602998
           vote |    .004957   .0219067     0.23   0.821     -.038083    .0479971
          _cons |   .2781446   .2421252     1.15   0.251     -.197559    .7538482
---------------------------------------------------------------------------------
(504 missing values generated)
file /var/folders/3r/sktq2lwj3fl3k94lykyp8wm80000gn/T//S_45066.000002 saved


----------------------------------------------------------------
Sensitivity results
----------------------------------------------------------------
        Rho at which ACME = 0            |     .2809
        R^2_M*R^2_Y* at which ACME = 0:  |     .0789
        R^2_M~R^2_Y~ at which ACME = 0:  |     .0649
----------------------------------------------------------------
95% Confidence interval

. twoway rarea _med_updelta0 _med_lodelta0 _med_rho, bcolor(gs14) || line _med_del
> ta0 _med_rho , lcolor(black) graphregion(color(white)) mcolor(black) ytitle("ACM
> E") xtitle("Sensitivity parameter: {&rho}") legend(off) title("ACME({&rho})")

. 
. 
. /*****************************************************
> Figure A3. Average Causal Mediation Effect of the Random Bonus Treatment on Know
> ledge Accuracy as a Function Degree of Violation of Sequential Ignorability Assu
> mption.
> ******************************************************/
. 
. medsens (regress minutes random_bonus_treatment k_correct education age income p
> oliticalinterest newsconsumption vote) (regress p_correct random_bonus_treatment
>  minutes k_correct education age income politicalinterest newsconsumption vote),
>  treat(random_bonus_treatment) mediate(minutes) sims(1000)
Dropping existing variable _med_rho
Dropping existing variable _med_delta0
Dropping existing variable _med_updelta0
Dropping existing variable _med_lodelta0
Dropping existing variable _med_delta1
Dropping existing variable _med_updelta1
Dropping existing variable _med_lodelta1

      Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(8, 497)       =      3.42
       Model |  829.042594         8  103.630324   Prob > F        =    0.0008
    Residual |  15038.0798       497  30.2577058   R-squared       =    0.0522
-------------+----------------------------------   Adj R-squared   =    0.0370
       Total |  15867.1224       505  31.4200443   Root MSE        =    5.5007

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
random_bonus_~t |   .9667697    .491631     1.97   0.050     .0008383    1.932701
      k_correct |   .3309001   .1796778     1.84   0.066    -.0221215    .6839217
      education |  -.0443541   .1960943    -0.23   0.821    -.4296301    .3409219
            age |   .0835987   .0213371     3.92   0.000     .0416767    .1255207
         income |  -.0268245    .161999    -0.17   0.869    -.3451117    .2914628
politicalinte~t |  -.1866277   .4261002    -0.44   0.662    -1.023807     .650552
newsconsumption |  -.6128047   .4128101    -1.48   0.138    -1.423873    .1982634
           vote |  -.0442688   .1313561    -0.34   0.736    -.3023506    .2138129
          _cons |   8.629887   1.352865     6.38   0.000     5.971848    11.28793
---------------------------------------------------------------------------------
(510 missing values generated)

      Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(9, 496)       =      3.75
       Model |  28.7703252         9   3.1967028   Prob > F        =    0.0001
    Residual |   422.87592       496  .852572419   R-squared       =    0.0637
-------------+----------------------------------   Adj R-squared   =    0.0467
       Total |  451.646245       505     .894349   Root MSE        =    .92335

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        minutes |   .0352699   .0075296     4.68   0.000     .0204761    .0500636
random_bonus_~t |   .1356353   .0828457     1.64   0.102    -.0271364    .2984071
      k_correct |   .0179504   .0302635     0.59   0.553      -.04151    .0774108
      education |    .027532   .0329181     0.84   0.403    -.0371441    .0922082
            age |  -.0016694   .0036365    -0.46   0.646    -.0088143    .0054755
         income |  -.0056505   .0271939    -0.21   0.835      -.05908     .047779
politicalinte~t |  -.1468532    .071539    -2.05   0.041    -.2874101   -.0062962
newsconsumption |   .1157169   .0694478     1.67   0.096    -.0207312    .2521651
           vote |  -.0252836    .022052    -1.15   0.252    -.0686104    .0180432
          _cons |   .4844804   .2362057     2.05   0.041     .0203934    .9485674
---------------------------------------------------------------------------------
(510 missing values generated)
file /var/folders/3r/sktq2lwj3fl3k94lykyp8wm80000gn/T//S_45066.000002 saved


----------------------------------------------------------------
Sensitivity results
----------------------------------------------------------------
        Rho at which ACME = 0            |     .2058
        R^2_M*R^2_Y* at which ACME = 0:  |     .0424
        R^2_M~R^2_Y~ at which ACME = 0:  |     .0376
----------------------------------------------------------------
95% Confidence interval

. twoway rarea _med_updelta0 _med_lodelta0 _med_rho, bcolor(gs14) || line _med_del
> ta0 _med_rho , lcolor(black) graphregion(color(white)) mcolor(black) ytitle("ACM
> E") xtitle("Sensitivity parameter: {&rho}") legend(off) title("ACME({&rho})")

. 
. 
. /*****************************************************
> Figure A4. Average Causal Mediation Effect of the Lottery Treatment on Knowledge
>  Accuracy as a Function Degree of Violation of Sequential Ignorability Assumptio
> n.
> ******************************************************/
. 
. medsens (regress minutes lottery_treatment k_correct education age income politi
> calinterest newsconsumption vote) (regress p_correct lottery_treatment minutes k
> _correct education age income politicalinterest newsconsumption vote), treat(lot
> tery_treatment) mediate(minutes) sims(1000)
Dropping existing variable _med_rho
Dropping existing variable _med_delta0
Dropping existing variable _med_updelta0
Dropping existing variable _med_lodelta0
Dropping existing variable _med_delta1
Dropping existing variable _med_updelta1
Dropping existing variable _med_lodelta1

      Source |       SS           df       MS      Number of obs   =       510
-------------+----------------------------------   F(8, 501)       =      2.84
       Model |  732.710853         8  91.5888566   Prob > F        =    0.0043
    Residual |  16144.3655       501  32.2242825   R-squared       =    0.0434
-------------+----------------------------------   Adj R-squared   =    0.0281
       Total |  16877.0764       509   33.157321   Root MSE        =    5.6766

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
lottery_treat~t |   .8347971   .5045131     1.65   0.099     -.156425    1.826019
      k_correct |   .4349527   .1883115     2.31   0.021     .0649752    .8049303
      education |  -.4578621   .2072158    -2.21   0.028    -.8649812    -.050743
            age |   .0542077   .0231654     2.34   0.020     .0086945    .0997209
         income |  -.1707744   .1731921    -0.99   0.325    -.5110467    .1694979
politicalinte~t |   .1449847   .4431302     0.33   0.744    -.7256377    1.015607
newsconsumption |  -.3433065   .4247615    -0.81   0.419     -1.17784    .4912269
           vote |  -.0920151   .1368372    -0.67   0.502    -.3608605    .1768303
          _cons |   9.917222   1.463046     6.78   0.000      7.04276    12.79168
---------------------------------------------------------------------------------
(506 missing values generated)

      Source |       SS           df       MS      Number of obs   =       510
-------------+----------------------------------   F(9, 500)       =      8.12
       Model |  59.0626776         9  6.56251974   Prob > F        =    0.0000
    Residual |  404.288303       500  .808576606   R-squared       =    0.1275
-------------+----------------------------------   Adj R-squared   =    0.1118
       Total |   463.35098       509  .910316268   Root MSE        =    .89921

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        minutes |   .0488209    .007077     6.90   0.000     .0349165    .0627252
lottery_treat~t |   .2715092   .0801355     3.39   0.001     .1140655     .428953
      k_correct |   .0686816   .0299879     2.29   0.022     .0097638    .1275994
      education |  -.0116164   .0329836    -0.35   0.725    -.0764199    .0531871
            age |  -.0026235   .0036895    -0.71   0.477    -.0098724    .0046253
         income |   .0075847   .0274611     0.28   0.783    -.0463686    .0615381
politicalinte~t |  -.0963241   .0702015    -1.37   0.171    -.2342505    .0416023
newsconsumption |   .0497423   .0673282     0.74   0.460    -.0825388    .1820234
           vote |  -.0108234   .0216855    -0.50   0.618    -.0534293    .0317825
          _cons |   .2753147   .2421481     1.14   0.256    -.2004384    .7510678
---------------------------------------------------------------------------------
(506 missing values generated)
file /var/folders/3r/sktq2lwj3fl3k94lykyp8wm80000gn/T//S_45066.000002 saved


----------------------------------------------------------------
Sensitivity results
----------------------------------------------------------------
        Rho at which ACME = 0            |     .2948
        R^2_M*R^2_Y* at which ACME = 0:  |     .0869
        R^2_M~R^2_Y~ at which ACME = 0:  |     .0725
----------------------------------------------------------------
95% Confidence interval

. twoway rarea _med_updelta0 _med_lodelta0 _med_rho, bcolor(gs14) || line _med_del
> ta0 _med_rho , lcolor(black) graphregion(color(white)) mcolor(black) ytitle("ACM
> E") xtitle("Sensitivity parameter: {&rho}") legend(off) title("ACME({&rho})")

. 
. 
. /*****************************************************
> Table A12. Direct Treatment Effects and Mediation Effects of Incentives on Knowl
> edge Accuracy, with Information Search (self-report) as mediating variable
> ******************************************************/
. 
. medeff (regress is_total bonus_treatment k_correct education age income politica
> linterest newsconsumption vote) (regress p_correct bonus_treatment is_total k_co
> rrect education age income politicalinterest newsconsumption vote), treat(bonus_
> treatment) mediate(is_total) sims(1000)
Using 0 and 1 as treatment values

      Source |       SS           df       MS      Number of obs   =       512
-------------+----------------------------------   F(8, 503)       =      2.45
       Model |  2.59822467         8  .324778084   Prob > F        =    0.0131
    Residual |  66.6617759       503  .132528381   R-squared       =    0.0375
-------------+----------------------------------   Adj R-squared   =    0.0222
       Total |  69.2600005       511  .135538162   Root MSE        =    .36404

---------------------------------------------------------------------------------
       is_total |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
bonus_treatment |   .1052195    .032328     3.25   0.001     .0417049    .1687341
      k_correct |   .0129105   .0120767     1.07   0.286    -.0108164    .0366375
      education |  -.0042455   .0132021    -0.32   0.748    -.0301836    .0216926
            age |    .003659   .0013863     2.64   0.009     .0009353    .0063826
         income |   .0115617   .0112174     1.03   0.303     -.010477    .0336004
politicalinte~t |   .0016959   .0291892     0.06   0.954    -.0556519    .0590437
newsconsumption |  -.0207877   .0286603    -0.73   0.469    -.0770963    .0355209
           vote |   -.004518   .0086545    -0.52   0.602    -.0215213    .0124853
          _cons |   .0009201   .0931764     0.01   0.992    -.1821427    .1839829
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       512
-------------+----------------------------------   F(9, 502)       =     10.45
       Model |   76.357035         9    8.484115   Prob > F        =    0.0000
    Residual |  407.517965       502  .811788775   R-squared       =    0.1578
-------------+----------------------------------   Adj R-squared   =    0.1427
       Total |     483.875       511  .946917808   Root MSE        =    .90099

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
bonus_treatment |   .2857301   .0808485     3.53   0.000     .1268869    .4445733
       is_total |   .9105748   .1103527     8.25   0.000     .6937647    1.127385
      k_correct |   .0413459   .0299231     1.38   0.168    -.0174441     .100136
      education |  -.0185027   .0326781    -0.57   0.572    -.0827054    .0456999
            age |  -.0041315   .0034547    -1.20   0.232    -.0109189    .0026559
         income |  -.0019945   .0277918    -0.07   0.943    -.0565971    .0526081
politicalinte~t |  -.0044237   .0722422    -0.06   0.951    -.1463579    .1375105
newsconsumption |   .0325875   .0709699     0.46   0.646    -.1068471    .1720222
           vote |   .0096023   .0214252     0.45   0.654    -.0324918    .0516963
          _cons |   .6364328   .2306072     2.76   0.006     .1833587    1.089507
---------------------------------------------------------------------------------
The number of observations in the data is less than the number of simulations. Exp
> anding the data to the number of simulations
----------------------------------------------------------------------------------
> --
        Effect                 |  Mean           [95% Conf. Interval]
-------------------------------+--------------------------------------------------
> --
        ACME                   |   .096125      .0355649      .1631494
        Direct Effect          |   .285449      .1281582      .4385049
        Total Effect           |   .381574      .2272901      .5499153
        % of Tot Eff mediated  |  .2504018      .1747999      .4229179
----------------------------------------------------------------------------------
> --

. medeff (regress is_total random_bonus_treatment k_correct education age income p
> oliticalinterest newsconsumption vote) (regress p_correct random_bonus_treatment
>  is_total k_correct education age income politicalinterest newsconsumption vote)
> , treat(random_bonus_treatment) mediate(is_total) sims(1000)
Using 0 and 1 as treatment values

      Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(8, 497)       =      1.43
       Model |  1.29212394         8  .161515492   Prob > F        =    0.1792
    Residual |  55.9423433       497  .112560047   R-squared       =    0.0226
-------------+----------------------------------   Adj R-squared   =    0.0068
       Total |  57.2344672       505  .113335579   Root MSE        =     .3355

---------------------------------------------------------------------------------
       is_total |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
random_bonus_~t |   .0397068   .0299856     1.32   0.186    -.0192074    .0986211
      k_correct |    .009202   .0109589     0.84   0.401    -.0123296    .0307335
      education |  -.0007805   .0119602    -0.07   0.948    -.0242794    .0227183
            age |   .0033267   .0013014     2.56   0.011     .0007698    .0058836
         income |   .0002664   .0098807     0.03   0.979    -.0191466    .0196794
politicalinte~t |  -.0030456   .0259888    -0.12   0.907     -.054107    .0480158
newsconsumption |  -.0141887   .0251782    -0.56   0.573    -.0636575    .0352801
           vote |  -.0122023   .0080117    -1.52   0.128    -.0279433    .0035387
          _cons |   .0693147   .0825142     0.84   0.401    -.0928049    .2314343
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(9, 496)       =     10.61
       Model |  72.9342073         9  8.10380082   Prob > F        =    0.0000
    Residual |  378.712038       496  .763532334   R-squared       =    0.1615
-------------+----------------------------------   Adj R-squared   =    0.1463
       Total |  451.646245       505     .894349   Root MSE        =     .8738

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
random_bonus_~t |   .1276393   .0782348     1.63   0.103    -.0260731    .2813517
       is_total |   1.060117    .116827     9.07   0.000     .8305804    1.289654
      k_correct |    .019866   .0285626     0.70   0.487    -.0362526    .0759846
      education |   .0267952   .0311503     0.86   0.390    -.0344077     .087998
            age |  -.0022476   .0034117    -0.66   0.510    -.0089507    .0044555
         income |   -.006879   .0257341    -0.27   0.789    -.0574402    .0436822
politicalinte~t |  -.1502068   .0676883    -2.22   0.027    -.2831979   -.0172157
newsconsumption |   .1091451   .0655971     1.66   0.097    -.0197374    .2380276
           vote |  -.0139091    .020915    -0.67   0.506     -.055002    .0271837
          _cons |   .7153738   .2150593     3.33   0.001     .2928344    1.137913
---------------------------------------------------------------------------------
The number of observations in the data is less than the number of simulations. Exp
> anding the data to the number of simulations
----------------------------------------------------------------------------------
> --
        Effect                 |  Mean           [95% Conf. Interval]
-------------------------------+--------------------------------------------------
> --
        ACME                   |  .0426215     -.0208894      .1082241
        Direct Effect          |  .1273672     -.0248384       .275475
        Total Effect           |  .1699887      .0130698      .3343384
        % of Tot Eff mediated  |  .2459092      .1156115      1.742561
----------------------------------------------------------------------------------
> --

. medeff (regress is_total lottery_treatment k_correct education age income politi
> calinterest newsconsumption vote) (regress p_correct lottery_treatment is_total 
> k_correct education age income politicalinterest newsconsumption vote), treat(lo
> ttery_treatment) mediate(is_total) sims(1000)
Using 0 and 1 as treatment values

      Source |       SS           df       MS      Number of obs   =       510
-------------+----------------------------------   F(8, 501)       =      0.66
       Model |  .562290308         8  .070286289   Prob > F        =    0.7298
    Residual |  53.6293966       501  .107044704   R-squared       =    0.0104
-------------+----------------------------------   Adj R-squared   =   -0.0054
       Total |  54.1916869       509  .106466968   Root MSE        =    .32718

---------------------------------------------------------------------------------
       is_total |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
lottery_treat~t |   .0097061   .0290779     0.33   0.739    -.0474236    .0668358
      k_correct |   .0020635   .0108534     0.19   0.849    -.0192603    .0233874
      education |   -.008276    .011943    -0.69   0.489    -.0317406    .0151885
            age |   .0011075   .0013351     0.83   0.407    -.0015157    .0037307
         income |   .0028509    .009982     0.29   0.775    -.0167609    .0224627
politicalinte~t |   .0220903   .0255401     0.86   0.387    -.0280885    .0722692
newsconsumption |  -.0356365   .0244814    -1.46   0.146    -.0837354    .0124623
           vote |  -.0125999   .0078867    -1.60   0.111     -.028095    .0028952
          _cons |   .1937522   .0843236     2.30   0.022     .0280808    .3594236
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       510
-------------+----------------------------------   F(9, 500)       =     11.85
       Model |  81.4852281         9  9.05391423   Prob > F        =    0.0000
    Residual |  381.865752       500  .763731505   R-squared       =    0.1759
-------------+----------------------------------   Adj R-squared   =    0.1610
       Total |   463.35098       509  .910316268   Root MSE        =    .87392

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
lottery_treat~t |   .3019214   .0776783     3.89   0.000     .1493054    .4545374
       is_total |   1.065652   .1193353     8.93   0.000     .8311916    1.300112
      k_correct |   .0877174   .0289915     3.03   0.003     .0307571    .1446776
      education |  -.0251503   .0319161    -0.79   0.431    -.0878565    .0375559
            age |  -.0011572   .0035687    -0.32   0.746    -.0081688    .0058544
         income |  -.0037907    .026665    -0.14   0.887      -.05618    .0485987
politicalinte~t |  -.1127864   .0682707    -1.65   0.099    -.2469191    .0213463
newsconsumption |   .0709579     .06553     1.08   0.279    -.0577902    .1997061
           vote |  -.0018886   .0211196    -0.09   0.929    -.0433827    .0396056
          _cons |   .5530099   .2264191     2.44   0.015     .1081598    .9978599
---------------------------------------------------------------------------------
The number of observations in the data is less than the number of simulations. Exp
> anding the data to the number of simulations
----------------------------------------------------------------------------------
> --
        Effect                 |  Mean           [95% Conf. Interval]
-------------------------------+--------------------------------------------------
> --
        ACME                   |  .0109445     -.0514363      .0738768
        Direct Effect          |  .3016512      .1505283      .4487054
        Total Effect           |  .3125957      .1546761      .4731398
        % of Tot Eff mediated  |  .0348785      .0231321      .0707599
----------------------------------------------------------------------------------
> --

. 
. save "jeps.dta", replace
file jeps.dta saved

. 
. 
. 
. 
. /***************************************
> PILOT STUDY
> ****************************************/
. clear

. pause on

. set more off

. use "pilot.dta"

. 
. /***************************************
> Table A15. Descriptive Statistics
> ****************************************/
. 
. estpost summarize p_correct minutes democrat republican ideology moderate_3 dem_
> agreement rep_agreement education income male politicalinterest newsconsumption 
> sq_total rel_attendance age white black hisp

             |  e(count)   e(sum_w)    e(mean)     e(Var)      e(sd)     e(min) 
-------------+------------------------------------------------------------------
   p_correct |       298        298   5.251678   1.630048   1.276733          1 
     minutes |       298        298   18.79508   110.2393   10.49949         .3 
    democrat |       298        298   .4765101   .2502881    .500288          0 
  republican |       298        298    .204698   .1633449   .4041594          0 
    ideology |       298        298   3.342282   3.141708   1.772486          1 
  moderate_3 |       298        298   .4127517   .2432039    .493157          0 
dem_agreem~t |       298        298   53.40268   919.2447   30.31905          0 
rep_agreem~t |       298        298   30.51007   870.0016   29.49579          0 
   education |       298        298   10.18792   1.856823   1.362653          7 
      income |       298        298   2.795302   2.096005   1.447759          1 
        male |       298        298   .6107383   .2385375    .488403          0 
politicali~t |       298        298    2.42953   .8451856   .9193398          0 
newsconsum~n |       298        298   2.399329   .9140736    .956072          0 
    sq_total |       298        298    1.88255   .1242063   .3524291          0 
rel_attend~e |       298        298          1   2.262626   1.504203          0 
         age |       298        298   38.57383   164.1376   12.81162         20 
       white |       298        298   .7315436   .1970488   .4439018          0 
       black |       298        298   .1073826   .0961743   .3101198          0 
        hisp |       298        298    .090604   .0826724    .287528          0 

             |    e(max)     e(sum) 
-------------+----------------------
   p_correct |         7       1565 
     minutes |  44.86666   5600.933 
    democrat |         1        142 
  republican |         1         61 
    ideology |         7        996 
  moderate_3 |         1        123 
dem_agreem~t |       100      15914 
rep_agreem~t |       100       9092 
   education |        13       3036 
      income |         7        833 
        male |         1        182 
politicali~t |         4        724 
newsconsum~n |         4        715 
    sq_total |         2        561 
rel_attend~e |         5        298 
         age |        77      11495 
       white |         1        218 
       black |         1         32 
        hisp |         1         27 

. esttab using "tableA15.tex", cells("count mean sd min max") noobs replace title(
> {Descriptive Statistics.}\label{tab1})
(output written to tableA15.tex)

. 
. 
. /***************************************
> Table A16. Descriptive Statistics of Correct Individual Prediction Questions
> ****************************************/
. 
. estpost summarize p1_correct p2_correct p3_correct p4_correct p5_correct p6_corr
> ect p7_correct p8_correct

             |  e(count)   e(sum_w)    e(mean)     e(Var)      e(sd)     e(min) 
-------------+------------------------------------------------------------------
  p1_correct |       298        298   .7449664   .1906311   .4366133          0 
  p2_correct |       298        298   .3221477   .2191038   .4680852          0 
  p3_correct |       298        298   .8557047   .1238899     .35198          0 
  p4_correct |       298        298   .8624161   .1190541   .3450421          0 
  p5_correct |       298        298   .8892617   .0988069   .3143356          0 
  p6_correct |       298        298    .647651   .2289675   .4785055          0 
  p7_correct |       298        298   .8422819   .1332904   .3650896          0 
  p8_correct |       298        298   .7348993   .1954783   .4421292          0 

             |    e(max)     e(sum) 
-------------+----------------------
  p1_correct |         1        222 
  p2_correct |         1         96 
  p3_correct |         1        255 
  p4_correct |         1        257 
  p5_correct |         1        265 
  p6_correct |         1        193 
  p7_correct |         1        251 
  p8_correct |         1        219 

. esttab using "tableA16.tex", cells("count mean sd min max") noobs replace title(
> {Descriptive Statistics of Individual Political Prediction Questions.}\label{tab
> 1})
(output written to tableA16.tex)

. 
. 
. 
. /*****************************************************
> Table A17. Determinants of Cognitive Effort as Measured by Time Spent (Minutes)
> ******************************************************/
. 
. eststo clear

. 
. /* Column 1 */
. 
. reg minutes i.treatment, r

Linear regression                               Number of obs     =        298
                                                F(3, 294)         =       5.66
                                                Prob > F          =     0.0009
                                                R-squared         =     0.0520
                                                Root MSE          =     10.275

---------------------------------------------------------------------------------
                |               Robust
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   5.002692   1.631828     3.07   0.002     1.791148    8.214236
Random Bonus..  |   4.222547   1.802905     2.34   0.020     .6743123    7.770782
Lottery Trea..  |  -.2454708   1.578969    -0.16   0.877    -3.352986    2.862045
                |
          _cons |   16.51484   1.168693    14.13   0.000     14.21478    18.81491
---------------------------------------------------------------------------------

. estimates store c1, title(column 1)

. 
. /* Column 2 */
. 
. reg minutes i.treatment democrat republican ideology moderate_3 dem_agreement re
> p_agreement, r

Linear regression                               Number of obs     =        298
                                                F(9, 288)         =       2.73
                                                Prob > F          =     0.0046
                                                R-squared         =     0.0677
                                                Root MSE          =     10.295

---------------------------------------------------------------------------------
                |               Robust
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   4.851816    1.68391     2.88   0.004     1.537485    8.166146
Random Bonus..  |   4.166536   1.808956     2.30   0.022     .6060852    7.726986
Lottery Trea..  |  -.5012308   1.587238    -0.32   0.752    -3.625288    2.622827
                |
       democrat |  -2.024801   1.679221    -1.21   0.229    -5.329904    1.280301
     republican |  -3.046931    2.54676    -1.20   0.233    -8.059554    1.965692
       ideology |  -.4292256   .6639225    -0.65   0.518    -1.735981      .87753
     moderate_3 |  -1.539985   1.365432    -1.13   0.260    -4.227477    1.147506
  dem_agreement |   .0148401   .0383702     0.39   0.699    -.0606815    .0903618
  rep_agreement |   .0560931   .0373824     1.50   0.135    -.0174844    .1296705
          _cons |    17.7861   3.829662     4.64   0.000     10.24843    25.32378
---------------------------------------------------------------------------------

. estimates store c2, title(column 2)

. 
. /* Column 3 */
. 
. reg minutes i.treatment democrat republican ideology moderate_3 dem_agreement re
> p_agreement education income male politicalinterest newsconsumption rel_attendan
> ce age white black hisp, r

Linear regression                               Number of obs     =        298
                                                F(19, 278)        =       2.83
                                                Prob > F          =     0.0001
                                                R-squared         =     0.1234
                                                Root MSE          =     10.161

---------------------------------------------------------------------------------
                |               Robust
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   5.078864   1.677328     3.03   0.003     1.776987    8.380741
Random Bonus..  |   4.996727   1.835766     2.72   0.007      1.38296    8.610494
Lottery Trea..  |  -.0781578   1.634843    -0.05   0.962    -3.296402    3.140086
                |
       democrat |  -1.303805   1.618853    -0.81   0.421    -4.490573    1.882963
     republican |  -2.243896   2.748397    -0.82   0.415     -7.65421    3.166417
       ideology |  -.5343997    .694565    -0.77   0.442    -1.901674    .8328751
     moderate_3 |  -.4978871   1.448499    -0.34   0.731    -3.349306    2.353532
  dem_agreement |   .0044383   .0391697     0.11   0.910    -.0726685    .0815451
  rep_agreement |   .0530347   .0371308     1.43   0.154    -.0200586    .1261281
      education |   -.259908   .4659232    -0.56   0.577    -1.177094    .6572777
         income |  -1.105699    .402787    -2.75   0.006    -1.898599   -.3127996
           male |   .0506948   1.337855     0.04   0.970    -2.582919    2.684309
politicalinte~t |   2.435902    1.20103     2.03   0.043     .0716334    4.800171
newsconsumption |  -1.677301    1.24695    -1.35   0.180    -4.131965    .7773633
 rel_attendance |  -.4381687   .3831435    -1.14   0.254      -1.1924    .3160623
            age |   .0441757   .0481903     0.92   0.360    -.0506885    .1390398
          white |   .2682824   1.418984     0.19   0.850    -2.525036      3.0616
          black |   2.502476    2.05846     1.22   0.225    -1.549673    6.554625
           hisp |   1.312897   2.361442     0.56   0.579    -3.335682    5.961476
          _cons |    19.4427   7.132306     2.73   0.007     5.402512    33.48289
---------------------------------------------------------------------------------

. estimates store c3, title(column 3)

. 
. /*Building the Table*/
. esttab c1 c2 c3 using "tableA17.tex", b(3) replace unstack nobaselevels label no
> gap se star (+ 0.1 * 0.05 ** 0.01 *** 0.001) r2 title({Determinants of Informati
> on Search as Measured by Time Spent (Minutes).}\label{tab1})
(output written to tableA17.tex)

. 
. 
. /*****************************************************
> Table A18. Determinants of Political Predictions
> ******************************************************/
. 
. eststo clear

. 
. /* Column 1 */
. 
. reg p_correct i.treatment, r

Linear regression                               Number of obs     =        298
                                                F(3, 294)         =       3.05
                                                Prob > F          =     0.0290
                                                R-squared         =     0.0327
                                                Root MSE          =     1.2621

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |  -.0163672   .2021001    -0.08   0.936    -.4141134     .381379
Random Bonus..  |    .198445   .2015365     0.98   0.326     -.198192    .5950821
Lottery Trea..  |  -.4366901   .2197352    -1.99   0.048    -.8691435   -.0042367
                |
          _cons |   5.315068   .1483811    35.82   0.000     5.023045    5.607092
---------------------------------------------------------------------------------

. estimates store c1, title(column 1)

. 
. /* Column 2 */
. 
. reg p_correct i.treatment democrat republican ideology moderate_3 dem_agreement 
> rep_agreement, r

Linear regression                               Number of obs     =        298
                                                F(9, 288)         =       2.11
                                                Prob > F          =     0.0289
                                                R-squared         =     0.0582
                                                Root MSE          =     1.2582

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .0332377   .1993739     0.17   0.868    -.3591771    .4256524
Random Bonus..  |   .2141409   .2017216     1.06   0.289    -.1828946    .6111765
Lottery Trea..  |  -.4213491   .2230722    -1.89   0.060    -.8604076    .0177094
                |
       democrat |   .0850118   .2042853     0.42   0.678    -.3170697    .4870932
     republican |   .1994712   .3415871     0.58   0.560    -.4728525    .8717949
       ideology |  -.0234796   .0983015    -0.24   0.811      -.21696    .1700008
     moderate_3 |  -.2311652     .18478    -1.25   0.212    -.5948556    .1325253
  dem_agreement |  -.0068529   .0038333    -1.79   0.075    -.0143977    .0006919
  rep_agreement |  -.0056412   .0045059    -1.25   0.212    -.0145098    .0032274
          _cons |   5.925169    .420887    14.08   0.000     5.096765    6.753574
---------------------------------------------------------------------------------

. estimates store c2, title(column 2)

. 
. /* Column 3 */
. reg p_correct i.treatment democrat republican ideology moderate_3 dem_agreement 
> rep_agreement education income male politicalinterest newsconsumption rel_attend
> ance age white black hisp, r

Linear regression                               Number of obs     =        298
                                                F(19, 278)        =       2.90
                                                Prob > F          =     0.0001
                                                R-squared         =     0.1417
                                                Root MSE          =     1.2226

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .0528934   .2167022     0.24   0.807    -.3736924    .4794791
Random Bonus..  |   .2471756   .2109881     1.17   0.242    -.1681616    .6625128
Lottery Trea..  |  -.3383079    .232898    -1.45   0.147    -.7967755    .1201597
                |
       democrat |   .0920421   .2036134     0.45   0.652    -.3087778     .492862
     republican |   .2870819   .3075365     0.93   0.351    -.3183142     .892478
       ideology |  -.0273593   .0911334    -0.30   0.764    -.2067585    .1520398
     moderate_3 |   -.151952   .1756107    -0.87   0.388    -.4976477    .1937437
  dem_agreement |  -.0064212   .0038054    -1.69   0.093    -.0139124    .0010699
  rep_agreement |  -.0022019   .0042246    -0.52   0.603    -.0105181    .0061143
      education |   .0921317   .0587366     1.57   0.118    -.0234933    .2077566
         income |   .0671932   .0537361     1.25   0.212    -.0385881    .1729745
           male |    .019778   .1556337     0.13   0.899    -.2865923    .3261482
politicalinte~t |   .0668425      .1477     0.45   0.651    -.2239099     .357595
newsconsumption |    .012407   .1527426     0.08   0.935    -.2882719    .3130859
 rel_attendance |  -.1456755    .053887    -2.70   0.007    -.2517538   -.0395971
            age |   .0110798   .0058886     1.88   0.061    -.0005121    .0226717
          white |  -.4257567   .1869566    -2.28   0.024    -.7937872   -.0577263
          black |  -.1310357   .2679148    -0.49   0.625    -.6584352    .3963637
           hisp |  -.4339218   .3041922    -1.43   0.155    -1.032735     .164891
          _cons |   4.474702   .7926767     5.65   0.000     2.914291    6.035113
---------------------------------------------------------------------------------

. estimates store c3, title(column 3)

. 
. /*Building the Table*/
. esttab c1 c2 c3 using "tableA18.tex", b(3) replace unstack nobaselevels label no
> gap se star (+ 0.1 * 0.05 ** 0.01 *** 0.001) r2 title({Determinants of Political
>  Predictions.}\label{tab1})
(output written to tableA18.tex)

. 
. 
. /*****************************************************
> Table A19. Determinants of Knowledge Accuracy, including Screening Questions
> ******************************************************/
. 
. eststo clear

. 
. /* Column 1 */
. 
. reg p_correct i.treatment sq_total, r

Linear regression                               Number of obs     =        298
                                                F(4, 293)         =       3.32
                                                Prob > F          =     0.0112
                                                R-squared         =     0.0454
                                                Root MSE          =     1.2559

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |  -.0237108   .1992451    -0.12   0.905    -.4158438    .3684221
Random Bonus..  |   .2255302   .2021322     1.12   0.265    -.1722849    .6233452
Lottery Trea..  |  -.4206508   .2177745    -1.93   0.054    -.8492514    .0079497
                |
       sq_total |   .4086987   .1895585     2.16   0.032     .0356298    .7817676
          _cons |   4.536861   .4014635    11.30   0.000     3.746744    5.326979
---------------------------------------------------------------------------------

. estimates store c1, title(column 1)

. 
. /* Column 2 */
. 
. reg p_correct i.treatment sq_total democrat republican ideology moderate_3 dem_a
> greement rep_agreement, r

Linear regression                               Number of obs     =        298
                                                F(10, 287)        =       2.51
                                                Prob > F          =     0.0066
                                                R-squared         =     0.0685
                                                Root MSE          =     1.2535

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .0247111   .1968214     0.13   0.900    -.3626854    .4121076
Random Bonus..  |   .2401477   .2034936     1.18   0.239    -.1603814    .6406768
Lottery Trea..  |  -.4106866     .22064    -1.86   0.064    -.8449644    .0235912
                |
       sq_total |   .3732331   .1904829     1.96   0.051    -.0016874    .7481537
       democrat |   .0648174    .202248     0.32   0.749      -.33326    .4628948
     republican |   .1844452    .341038     0.54   0.589    -.4868077    .8556981
       ideology |  -.0334878   .0982102    -0.34   0.733    -.2267915    .1598159
     moderate_3 |  -.2212951   .1860622    -1.19   0.235    -.5875147    .1449244
  dem_agreement |   -.006776   .0037606    -1.80   0.073    -.0141778    .0006258
  rep_agreement |  -.0047149    .004581    -1.03   0.304    -.0137315    .0043017
          _cons |   5.225341   .5487849     9.52   0.000     4.145187    6.305495
---------------------------------------------------------------------------------

. estimates store c2, title(column 2)

. 
. /* Column 3 */
. reg p_correct i.treatment sq_total democrat republican ideology moderate_3 dem_a
> greement rep_agreement education income male politicalinterest newsconsumption r
> el_attendance age white black hisp, r

Linear regression                               Number of obs     =        298
                                                F(20, 277)        =       2.94
                                                Prob > F          =     0.0000
                                                R-squared         =     0.1487
                                                Root MSE          =     1.2198

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .0394557   .2138589     0.18   0.854    -.3815394    .4604508
Random Bonus..  |   .2584115   .2108243     1.23   0.221    -.1566098    .6734328
Lottery Trea..  |  -.3348683   .2295735    -1.46   0.146    -.7867986    .1170621
                |
       sq_total |   .3139681   .2016713     1.56   0.121     -.083035    .7109712
       democrat |   .0735729   .2017114     0.36   0.716    -.3235092    .4706549
     republican |   .2642538   .3068952     0.86   0.390    -.3398893     .868397
       ideology |  -.0352112   .0909163    -0.39   0.699    -.2141859    .1437635
     moderate_3 |  -.1464421    .176877    -0.83   0.408     -.494636    .2017517
  dem_agreement |  -.0063475   .0037605    -1.69   0.093    -.0137504    .0010554
  rep_agreement |  -.0014311    .004293    -0.33   0.739    -.0098821    .0070199
      education |   .0952505   .0578954     1.65   0.101    -.0187205    .2092214
         income |   .0641033   .0537725     1.19   0.234    -.0417514     .169958
           male |   .0198232   .1552286     0.13   0.898    -.2857543    .3254008
politicalinte~t |   .0388336   .1510171     0.26   0.797    -.2584535    .3361206
newsconsumption |   .0402743   .1601166     0.25   0.802    -.2749257    .3554742
 rel_attendance |  -.1363145   .0537326    -2.54   0.012    -.2420906   -.0305384
            age |   .0110271   .0058646     1.88   0.061    -.0005176    .0225719
          white |  -.4046303   .1823323    -2.22   0.027    -.7635632   -.0456973
          black |  -.1093515   .2596398    -0.42   0.674    -.6204694    .4017664
           hisp |  -.4374102   .3051529    -1.43   0.153    -1.038124    .1633031
          _cons |   3.846681   .8153146     4.72   0.000     2.241681    5.451681
---------------------------------------------------------------------------------

. estimates store c3, title(column 3)

. 
. /*Building the Table*/
. esttab c1 c2 c3 using "tableA19.tex", b(3) replace unstack nobaselevels label no
> gap se star (+ 0.1 * 0.05 ** 0.01 *** 0.001) r2 title({Determinants of Correct P
> redictions, including Screening Questions.}\label{tab1})
(output written to tableA19.tex)

. 
. 
. /*****************************************************
> Table A20. Determinants of Knowledge Accuracy, Pooled Across Treatments
> ******************************************************/
. 
. eststo clear

. 
. /* Column 1 */
. 
. reg p_correct treatment_group, r

Linear regression                               Number of obs     =        298
                                                F(1, 296)         =       0.24
                                                Prob > F          =     0.6235
                                                R-squared         =     0.0008
                                                Root MSE          =     1.2784

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
treatment_group |  -.0839574   .1708393    -0.49   0.623     -.420171    .2522563
          _cons |   5.315068   .1478789    35.94   0.000     5.024041    5.606096
---------------------------------------------------------------------------------

. estimates store c1, title(column 1)

. 
. /* Column 2 */
. 
. reg p_correct treatment_group democrat republican ideology moderate_3 dem_agreem
> ent rep_agreement, r

Linear regression                               Number of obs     =        298
                                                F(7, 290)         =       1.19
                                                Prob > F          =     0.3108
                                                R-squared         =     0.0259
                                                Root MSE          =     1.2752

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
treatment_group |  -.0560862   .1719441    -0.33   0.745    -.3945027    .2823302
       democrat |   .0923714   .2090027     0.44   0.659    -.3189832    .5037259
     republican |   .2130471   .3537074     0.60   0.547     -.483112    .9092062
       ideology |  -.0020044   .1027981    -0.02   0.984    -.2043294    .2003206
     moderate_3 |  -.2364353      .1875    -1.26   0.208    -.6054687    .1325981
  dem_agreement |  -.0059549   .0038095    -1.56   0.119    -.0134526    .0015428
  rep_agreement |  -.0066571   .0045222    -1.47   0.142    -.0155576    .0022434
          _cons |   5.831804   .4219588    13.82   0.000     5.001314    6.662294
---------------------------------------------------------------------------------

. estimates store c2, title(column 2)

. 
. /* Column 3 */
. reg p_correct treatment_group democrat republican ideology moderate_3 dem_agreem
> ent rep_agreement education income male politicalinterest newsconsumption rel_at
> tendance age white black hisp, r

Linear regression                               Number of obs     =        298
                                                F(17, 280)        =       2.45
                                                Prob > F          =     0.0013
                                                R-squared         =     0.1157
                                                Root MSE          =     1.2365

---------------------------------------------------------------------------------
                |               Robust
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
treatment_group |  -.0093577   .1873583    -0.05   0.960    -.3781674    .3594521
       democrat |   .0961798   .2070978     0.46   0.643    -.3114864    .5038461
     republican |   .2996831   .3148847     0.95   0.342    -.3201586    .9195249
       ideology |  -.0094662   .0937067    -0.10   0.920    -.1939253    .1749929
     moderate_3 |  -.1564454   .1747152    -0.90   0.371    -.5003675    .1874768
  dem_agreement |  -.0056576   .0038028    -1.49   0.138    -.0131433    .0018281
  rep_agreement |  -.0029592   .0042207    -0.70   0.484    -.0112675    .0053491
      education |   .0979279    .059019     1.66   0.098    -.0182494    .2141051
         income |    .071655   .0531765     1.35   0.179    -.0330214    .1763315
           male |   -.014884   .1583614    -0.09   0.925     -.326614     .296846
politicalinte~t |   .0355045   .1443217     0.25   0.806    -.2485887    .3195977
newsconsumption |   .0313082   .1514612     0.21   0.836     -.266839    .3294554
 rel_attendance |  -.1473494   .0540447    -2.73   0.007    -.2537348   -.0409639
            age |   .0129882   .0059371     2.19   0.030     .0013011    .0246752
          white |  -.4184382   .1907416    -2.19   0.029    -.7939077   -.0429687
          black |   -.122831    .274143    -0.45   0.654    -.6624739    .4168118
           hisp |  -.4356188   .3177023    -1.37   0.171    -1.061007    .1897694
          _cons |    4.29504   .8062582     5.33   0.000     2.707943    5.882137
---------------------------------------------------------------------------------

. estimates store c3, title(column 3)

. 
. /*Building the Table*/
. esttab c1 c2 c3 using "tableA20.tex", b(3) replace unstack nobaselevels label no
> gap se star (+ 0.1 * 0.05 ** 0.01 *** 0.001) r2 title({Determinants of Correct P
> redictions, Pooled Across Treatments.}\label{tab1})
(output written to tableA20.tex)

. 
. 
. /*****************************************************
> Table A21. Determinants of Correct Individual Predictions (Logit)
> ******************************************************/
. 
. eststo clear

. 
. /* Column 1 */
. 
. logit p1_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -169.20375  
Iteration 1:   log pseudolikelihood = -168.64226  
Iteration 2:   log pseudolikelihood = -168.64115  
Iteration 3:   log pseudolikelihood = -168.64115  

Logistic regression                             Number of obs     =        298
                                                Wald chi2(3)      =       1.13
                                                Prob > chi2       =     0.7697
Log pseudolikelihood = -168.64115               Pseudo R2         =     0.0033

---------------------------------------------------------------------------------
                |               Robust
     p1_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .1426206   .3796558     0.38   0.707     -.601491    .8867322
Random Bonus..  |   .1652929   .3847261     0.43   0.667    -.5887565    .9193422
Lottery Trea..  |  -.1843438   .3691785    -0.50   0.618    -.9079204    .5392328
                |
          _cons |   1.044545   .2671884     3.91   0.000     .5208654    1.568225
---------------------------------------------------------------------------------

. estimates store c1, title(column 1)

. 
. /* Column 2 */
. 
. logit p2_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -187.28636  
Iteration 1:   log pseudolikelihood = -185.43555  
Iteration 2:   log pseudolikelihood =  -185.4299  
Iteration 3:   log pseudolikelihood =  -185.4299  

Logistic regression                             Number of obs     =        298
                                                Wald chi2(3)      =       3.73
                                                Prob > chi2       =     0.2919
Log pseudolikelihood =  -185.4299               Pseudo R2         =     0.0099

---------------------------------------------------------------------------------
                |               Robust
     p2_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |  -.4934871   .3449423    -1.43   0.153    -1.169562    .1825874
Random Bonus..  |  -.4363287    .346523    -1.26   0.208    -1.115501    .2428439
Lottery Trea..  |   -.633249   .3543006    -1.79   0.074    -1.327665    .0611673
                |
          _cons |  -.3600027   .2382849    -1.51   0.131    -.8270325     .107027
---------------------------------------------------------------------------------

. estimates store c2, title(column 2)

. 
. /* Column 3 */
. 
. logit p3_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -122.98005  
Iteration 1:   log pseudolikelihood = -121.84925  
Iteration 2:   log pseudolikelihood = -121.83577  
Iteration 3:   log pseudolikelihood = -121.83576  

Logistic regression                             Number of obs     =        298
                                                Wald chi2(3)      =       2.27
                                                Prob > chi2       =     0.5186
Log pseudolikelihood = -121.83576               Pseudo R2         =     0.0093

---------------------------------------------------------------------------------
                |               Robust
     p3_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   -.405465   .4898036    -0.83   0.408    -1.365463    .5545325
Random Bonus..  |   -.117783   .5174736    -0.23   0.820    -1.132013    .8964466
Lottery Trea..  |  -.6396585   .4787997    -1.34   0.182    -1.578089    .2987716
                |
          _cons |   2.094946   .3753096     5.58   0.000     1.359352    2.830539
---------------------------------------------------------------------------------

. estimates store c3, title(column 3)

. 
. /* Column 4 */
. 
. logit p4_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -119.36485  
Iteration 1:   log pseudolikelihood = -117.03277  
Iteration 2:   log pseudolikelihood = -116.94137  
Iteration 3:   log pseudolikelihood =  -116.9413  
Iteration 4:   log pseudolikelihood =  -116.9413  

Logistic regression                             Number of obs     =        298
                                                Wald chi2(3)      =       5.04
                                                Prob > chi2       =     0.1691
Log pseudolikelihood =  -116.9413               Pseudo R2         =     0.0203

---------------------------------------------------------------------------------
                |               Robust
     p4_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .0597192   .5299243     0.11   0.910    -.9789132    1.098352
Random Bonus..  |   -.117783   .5174736    -0.23   0.820    -1.132013    .8964466
Lottery Trea..  |  -.8070914   .4699651    -1.72   0.086    -1.728206    .1140232
                |
          _cons |   2.094946   .3753096     5.58   0.000     1.359352    2.830539
---------------------------------------------------------------------------------

. estimates store c4, title(column 4)

. 
. /* Column 5 */
. 
. logit p5_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -103.72071  
Iteration 1:   log pseudolikelihood = -102.06341  
Iteration 2:   log pseudolikelihood = -102.02399  
Iteration 3:   log pseudolikelihood = -102.02394  
Iteration 4:   log pseudolikelihood = -102.02394  

Logistic regression                             Number of obs     =        298
                                                Wald chi2(3)      =       3.18
                                                Prob > chi2       =     0.3649
Log pseudolikelihood = -102.02394               Pseudo R2         =     0.0164

---------------------------------------------------------------------------------
                |               Robust
     p5_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   .4620355   .5233881     0.88   0.377    -.5637864    1.487857
Random Bonus..  |    .784119   .5757414     1.36   0.173    -.3443134    1.912551
Lottery Trea..  |  -.0953102   .4726572    -0.20   0.840    -1.021701    .8310809
                |
          _cons |    1.84055   .3409738     5.40   0.000     1.172253    2.508846
---------------------------------------------------------------------------------

. estimates store c5, title(column 5)

. 
. /* Column 6 */
. 
. logit p6_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -193.36882  
Iteration 1:   log pseudolikelihood = -192.77241  
Iteration 2:   log pseudolikelihood = -192.77201  
Iteration 3:   log pseudolikelihood = -192.77201  

Logistic regression                             Number of obs     =        298
                                                Wald chi2(3)      =       1.20
                                                Prob > chi2       =     0.7534
Log pseudolikelihood = -192.77201               Pseudo R2         =     0.0031

---------------------------------------------------------------------------------
                |               Robust
     p6_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |   -.257671   .3394365    -0.76   0.448    -.9229544    .4076124
Random Bonus..  |   .0206193   .3487832     0.06   0.953    -.6629832    .7042218
Lottery Trea..  |    .081644   .3505887     0.23   0.816    -.6054973    .7687853
                |
          _cons |   .6523252    .247059     2.64   0.008     .1680984    1.136552
---------------------------------------------------------------------------------

. estimates store c6, title(column 6)

. 
. /* Column 7 */
. 
. logit p7_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -129.88823  
Iteration 1:   log pseudolikelihood = -126.58651  
Iteration 2:   log pseudolikelihood = -126.50089  
Iteration 3:   log pseudolikelihood = -126.50081  
Iteration 4:   log pseudolikelihood = -126.50081  

Logistic regression                             Number of obs     =        298
                                                Wald chi2(3)      =       6.43
                                                Prob > chi2       =     0.0926
Log pseudolikelihood = -126.50081               Pseudo R2         =     0.0261

---------------------------------------------------------------------------------
                |               Robust
     p7_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |    .583803   .4635902     1.26   0.208    -.3248172    1.492423
Random Bonus..  |   .8203024   .4969799     1.65   0.099    -.1537604    1.794365
Lottery Trea..  |  -.2286422   .4065708    -0.56   0.574    -1.025506    .5682219
                |
          _cons |    1.43848    .297784     4.83   0.000     .8548343    2.022126
---------------------------------------------------------------------------------

. estimates store c7, title(column 7)

. 
. /* Column 8 */
. 
. logit p8_correct i.treatment, r

Iteration 0:   log pseudolikelihood = -172.34077  
Iteration 1:   log pseudolikelihood = -169.44212  
Iteration 2:   log pseudolikelihood = -169.41636  
Iteration 3:   log pseudolikelihood = -169.41635  

Logistic regression                             Number of obs     =        298
                                                Wald chi2(3)      =       5.26
                                                Prob > chi2       =     0.1538
Log pseudolikelihood = -169.41635               Pseudo R2         =     0.0170

---------------------------------------------------------------------------------
                |               Robust
     p8_correct |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      treatment |
Bonus Treatm..  |  -.0532315   .3595559    -0.15   0.882     -.757948    .6514851
Random Bonus..  |   .7355064   .4084999     1.80   0.072    -.0651386    1.536151
Lottery Trea..  |  -.1103899   .3610726    -0.31   0.760    -.8180792    .5972994
                |
          _cons |   .9067213   .2589882     3.50   0.000     .3991137    1.414329
---------------------------------------------------------------------------------

. estimates store c8, title(column 8)

. 
. 
. /*Building the Figure*/
. esttab c1 c2 c3 c4 c5 c6 c7 c8 using "tableA21.tex", b(3) replace unstack nobase
> levels label nogap se star (+ 0.1 * 0.05 ** 0.01 *** 0.001) pr2 title({Determina
> nts of Correct Individual Predictions (Logit).}\label{tab1})
(output written to tableA21.tex)

. 
. 
. /*****************************************************
> Table A22. Randomization Check: F-test of Joint Orthogonality
> ******************************************************/
. 
. orth_out democrat republican ideology moderate_3 dem_agreement rep_agreement edu
> cation income male politicalinterest newsconsumption rel_attendance age white bl
> ack hisp using "tableA22.tex", by(treatment) se test latex replace

                                       0:  Bonus Tre~t:  Random Bo~t:
                                       _             _             _
             Democrat:mean         0.466         0.481         0.527
                        se         0.059         0.057         0.058
           Republican:mean         0.260         0.156         0.189
                        se         0.052         0.042         0.046
   Political Ideology:mean         3.438         3.182         3.351
                        se         0.215         0.191         0.214
             Moderate:mean         0.384         0.468         0.378
                        se         0.057         0.057         0.057
Dem. Policy Agreement:mean        51.795        57.117        55.189
                        se         3.594         3.366         3.679
Rep. Policy Agreement:mean        31.425        27.909        29.068
                        se         3.590         3.272         3.533
            Education:mean         9.890        10.429        10.324
                        se         0.184         0.131         0.147
               Income:mean         2.836         2.844         2.797
                        se         0.182         0.168         0.161
                 Male:mean         0.534         0.662         0.541
                        se         0.059         0.054         0.058
   Political Interest:mean         2.411         2.623         2.257
                        se         0.095         0.091         0.114
     News Consumption:mean         2.315         2.571         2.338
                        se         0.108         0.097         0.111
 Religious Attendance:mean         0.658         1.130         1.108
                        se         0.145         0.183         0.175
                  Age:mean        38.726        38.221        40.986
                        se         1.550         1.470         1.530
                White:mean         0.726         0.662         0.784
                        se         0.053         0.054         0.048
                Black:mean         0.151         0.143         0.068
                        se         0.042         0.040         0.029
      Hispanic/Latino:mean         0.068         0.143         0.054
                        se         0.030         0.040         0.026

                             Lottery T~t:  p-value f~y:
                                       _             _
             Democrat:mean         0.432         0.715
                        se         0.058             .
           Republican:mean         0.216         0.446
                        se         0.048             .
   Political Ideology:mean         3.405         0.817
                        se         0.205             .
             Moderate:mean         0.419         0.667
                        se         0.058             .
Dem. Policy Agreement:mean        49.338         0.401
                        se         3.414             .
Rep. Policy Agreement:mean        33.757         0.630
                        se         3.306             .
            Education:mean        10.095         0.072
                        se         0.163             .
               Income:mean         2.703         0.931
                        se         0.162             .
                 Male:mean         0.703         0.078
                        se         0.053             .
   Political Interest:mean         2.419         0.107
                        se         0.122             .
     News Consumption:mean         2.365         0.327
                        se         0.126             .
 Religious Attendance:mean         1.095         0.169
                        se         0.187             .
                  Age:mean        36.378         0.182
                        se         1.362             .
                White:mean         0.757         0.371
                        se         0.050             .
                Black:mean         0.068         0.182
                        se         0.029             .
      Hispanic/Latino:mean         0.095         0.243
                        se         0.034             .

. 
. 
. /*****************************************************
> Table A23. Randomization Check: F-test of Joint Orthogonality
> ******************************************************/
. 
. orth_out democrat republican ideology moderate_3 dem_agreement rep_agreement edu
> cation income male politicalinterest newsconsumption rel_attendance age white bl
> ack hisp using "tableA23.tex", by(treatment) test pcompare count latex replace

                                       0:  Bonus Tre~t:  Random Bo~t:
                                       _             _             _
             Democrat:mean         0.466         0.481         0.527
           Republican:mean         0.260         0.156         0.189
   Political Ideology:mean         3.438         3.182         3.351
             Moderate:mean         0.384         0.468         0.378
Dem. Policy Agreement:mean        51.795        57.117        55.189
Rep. Policy Agreement:mean        31.425        27.909        29.068
            Education:mean         9.890        10.429        10.324
               Income:mean         2.836         2.844         2.797
                 Male:mean         0.534         0.662         0.541
   Political Interest:mean         2.411         2.623         2.257
     News Consumption:mean         2.315         2.571         2.338
 Religious Attendance:mean         0.658         1.130         1.108
                  Age:mean        38.726        38.221        40.986
                White:mean         0.726         0.662         0.784
                Black:mean         0.151         0.143         0.068
      Hispanic/Latino:mean         0.068         0.143         0.054
                       N:_        73.000        77.000        74.000

                             Lottery T~t:  (1) vs. (~e:  (1) vs. (~e:
                                       _             _             _
             Democrat:mean         0.432         0.858         0.461
           Republican:mean         0.216         0.116         0.305
   Political Ideology:mean         3.405         0.372         0.774
             Moderate:mean         0.419         0.302         0.949
Dem. Policy Agreement:mean        49.338         0.281         0.510
Rep. Policy Agreement:mean        33.757         0.470         0.640
            Education:mean        10.095         0.017         0.066
               Income:mean         2.703         0.973         0.875
                 Male:mean         0.703         0.111         0.940
   Political Interest:mean         2.419         0.108         0.301
     News Consumption:mean         2.365         0.079         0.884
 Religious Attendance:mean         1.095         0.047         0.049
                  Age:mean        36.378         0.813         0.301
                White:mean         0.757         0.401         0.419
                Black:mean         0.068         0.893         0.107
      Hispanic/Latino:mean         0.095         0.142         0.717
                       N:_        74.000             .             .

                             (1) vs. (~e:  (2) vs. (~e:  (2) vs. (~e:
                                       _             _             _
             Democrat:mean         0.687         0.571         0.556
           Republican:mean         0.534         0.590         0.343
   Political Ideology:mean         0.912         0.554         0.426
             Moderate:mean         0.665         0.271         0.551
Dem. Policy Agreement:mean         0.621         0.699         0.107
Rep. Policy Agreement:mean         0.633         0.810         0.211
            Education:mean         0.407         0.597         0.112
               Income:mean         0.586         0.841         0.546
                 Male:mean         0.036         0.128         0.597
   Political Interest:mean         0.959         0.012         0.178
     News Consumption:mean         0.765         0.114         0.193
 Religious Attendance:mean         0.067         0.932         0.893
                  Age:mean         0.257         0.194         0.360
                White:mean         0.673         0.097         0.204
                Black:mean         0.107         0.135         0.135
      Hispanic/Latino:mean         0.566         0.069         0.364
                       N:_             .             .             .

                             (3) vs. (~e:  p-value f~y:
                                       _             _
             Democrat:mean         0.252         0.715
           Republican:mean         0.685         0.446
   Political Ideology:mean         0.856         0.817
             Moderate:mean         0.617         0.667
Dem. Policy Agreement:mean         0.246         0.401
Rep. Policy Agreement:mean         0.334         0.630
            Education:mean         0.297         0.072
               Income:mean         0.679         0.931
                 Male:mean         0.042         0.078
   Political Interest:mean         0.332         0.107
     News Consumption:mean         0.872         0.327
 Religious Attendance:mean         0.958         0.169
                  Age:mean         0.026         0.182
                White:mean         0.698         0.371
                Black:mean         1.000         0.182
      Hispanic/Latino:mean         0.351         0.243
                       N:_             .             .

. 
. 
. /*****************************************************
> Table A24. Direct Treatment Effects and Mediation Effects of Incentives on the N
> umber of Correct Answers for Prediction Questions
> ******************************************************/
. 
. medeff (regress minutes bonus_treatment education age income politicalinterest n
> ewsconsumption vote) (regress p_correct bonus_treatment minutes education age in
> come politicalinterest newsconsumption vote), treat(bonus_treatment) mediate(min
> utes) sims(1000)
Using 0 and 1 as treatment values

      Source |       SS           df       MS      Number of obs   =       298
-------------+----------------------------------   F(7, 290)       =      3.47
       Model |  2533.13109         7   361.87587   Prob > F        =    0.0014
    Residual |  30207.9445       290  104.165326   R-squared       =    0.0774
-------------+----------------------------------   Adj R-squared   =    0.0551
       Total |  32741.0756       297  110.239312   Root MSE        =    10.206

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
bonus_treatment |   3.669973   1.369607     2.68   0.008     .9743439    6.365603
      education |  -.4407015   .4756744    -0.93   0.355    -1.376913    .4955104
            age |   .0513838   .0483968     1.06   0.289    -.0438697    .1466372
         income |  -1.247928   .4328745    -2.88   0.004    -2.099902   -.3959543
politicalinte~t |   1.584478   1.159677     1.37   0.173    -.6979729     3.86693
newsconsumption |  -1.092546   1.130865    -0.97   0.335    -3.318289    1.133197
           vote |  -.3584156   .3309038    -1.08   0.280    -1.009693     .292862
          _cons |   23.56129   5.352416     4.40   0.000     13.02678     34.0958
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       298
-------------+----------------------------------   F(8, 289)       =      2.72
       Model |  33.9113787         8  4.23892234   Prob > F        =    0.0066
    Residual |  450.212782       289   1.5578297   R-squared       =    0.0700
-------------+----------------------------------   Adj R-squared   =    0.0443
       Total |  484.124161       297  1.63004768   Root MSE        =    1.2481

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
bonus_treatment |  -.0427229   .1695529    -0.25   0.801     -.376438    .2909921
        minutes |   .0136451   .0071812     1.90   0.058     -.000489    .0277793
      education |   .0948597   .0582573     1.63   0.105    -.0198026     .209522
            age |   .0126213     .00593     2.13   0.034     .0009498    .0242929
         income |   .0893651   .0536903     1.66   0.097    -.0163086    .1950387
politicalinte~t |  -.0075844   .1422751    -0.05   0.958    -.2876112    .2724424
newsconsumption |   .0886426   .1385182     0.64   0.523    -.1839898     .361275
           vote |  -.0270167   .0405487    -0.67   0.506    -.1068249    .0527915
          _cons |    3.18027   .6760731     4.70   0.000     1.849619    4.510922
---------------------------------------------------------------------------------
The number of observations in the data is less than the number of simulations. Exp
> anding the data to the number of simulations
----------------------------------------------------------------------------------
> --
        Effect                 |  Mean           [95% Conf. Interval]
-------------------------------+--------------------------------------------------
> --
        ACME                   |  .0501292       .000767      .1213882
        Direct Effect          | -.0397039     -.3843996      .2941244
        Total Effect           |  .0104253     -.3280735       .336667
        % of Tot Eff mediated  |  .1338623     -8.007814      4.741707
----------------------------------------------------------------------------------
> --

. medeff (regress minutes random_bonus_treatment education age income politicalint
> erest newsconsumption vote) (regress p_correct random_bonus_treatment minutes ed
> ucation age income politicalinterest newsconsumption vote), treat(random_bonus_t
> reatment) mediate(minutes) sims(1000)
Using 0 and 1 as treatment values

      Source |       SS           df       MS      Number of obs   =       298
-------------+----------------------------------   F(7, 290)       =      3.05
       Model |  2245.22313         7  320.746161   Prob > F        =    0.0041
    Residual |  30495.8524       290  105.158112   R-squared       =    0.0686
-------------+----------------------------------   Adj R-squared   =    0.0461
       Total |  32741.0756       297  110.239312   Root MSE        =    10.255

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
random_bonus_~t |    2.93214   1.401909     2.09   0.037     .1729343    5.691346
      education |  -.3582925    .476107    -0.75   0.452    -1.295356    .5787709
            age |    .031843   .0489138     0.65   0.516     -.064428    .1281141
         income |  -1.273576   .4348218    -2.93   0.004    -2.129383   -.4177697
politicalinte~t |   2.151009    1.17329     1.83   0.068    -.1582343    4.460252
newsconsumption |  -1.262837    1.13899    -1.11   0.268    -3.504571    .9788973
           vote |  -.3548892   .3324965    -1.07   0.287    -1.009301    .2995231
          _cons |    22.7902   5.376619     4.24   0.000     12.20806    33.37234
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       298
-------------+----------------------------------   F(8, 289)       =      3.06
       Model |  37.7838323         8  4.72297904   Prob > F        =    0.0025
    Residual |  446.340329       289   1.5444302   R-squared       =    0.0780
-------------+----------------------------------   Adj R-squared   =    0.0525
       Total |  484.124161       297  1.63004768   Root MSE        =    1.2428

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
random_bonus_~t |   .2744854   .1711724     1.60   0.110    -.0624172    .6113879
        minutes |   .0119727   .0071165     1.68   0.094    -.0020339    .0259794
      education |   .0891337   .0577552     1.54   0.124    -.0245405    .2028078
            age |   .0116176   .0059321     1.96   0.051    -.0000581    .0232933
         income |   .0875878   .0534693     1.64   0.102    -.0176508    .1928264
politicalinte~t |   .0245074   .1430113     0.17   0.864    -.2569683    .3059831
newsconsumption |    .071376   .1383251     0.52   0.606    -.2008764    .3436284
           vote |  -.0267729   .0403739    -0.66   0.508    -.1062371    .0526914
          _cons |   3.197342   .6714678     4.76   0.000     1.875755    4.518929
---------------------------------------------------------------------------------
The number of observations in the data is less than the number of simulations. Exp
> anding the data to the number of simulations
----------------------------------------------------------------------------------
> --
        Effect                 |  Mean           [95% Conf. Interval]
-------------------------------+--------------------------------------------------
> --
        ACME                   |  .0351178     -.0045441       .097587
        Direct Effect          |  .2775333     -.0704548      .6145501
        Total Effect           |  .3126511     -.0328323      .6451815
        % of Tot Eff mediated  |   .108966     -.2466658      .6962006
----------------------------------------------------------------------------------
> --

. medeff (regress minutes lottery_treatment education age income politicalinterest
>  newsconsumption vote) (regress p_correct lottery_treatment minutes education ag
> e income politicalinterest newsconsumption vote), treat(lottery_treatment) media
> te(minutes) sims(1000)
Using 0 and 1 as treatment values

      Source |       SS           df       MS      Number of obs   =       298
-------------+----------------------------------   F(7, 290)       =      3.34
       Model |   2442.4601         7  348.922872   Prob > F        =    0.0019
    Residual |  30298.6155       290  104.477984   R-squared       =    0.0746
-------------+----------------------------------   Adj R-squared   =    0.0523
       Total |  32741.0756       297  110.239312   Root MSE        =    10.221

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
lottery_treat~t |   -3.45935   1.379243    -2.51   0.013    -6.173945   -.7447551
      education |  -.3351698   .4742264    -0.71   0.480    -1.268532    .5981923
            age |    .032103   .0486373     0.66   0.510    -.0636239    .1278299
         income |  -1.316636    .433745    -3.04   0.003    -2.170324    -.462949
politicalinte~t |   1.863629   1.158474     1.61   0.109    -.4164531    4.143711
newsconsumption |  -1.113926   1.132578    -0.98   0.326    -3.343041     1.11519
           vote |  -.3550324   .3314115    -1.07   0.285    -1.007309    .2972445
          _cons |    24.5934   5.391296     4.56   0.000     13.98238    35.20443
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       298
-------------+----------------------------------   F(8, 289)       =      3.46
       Model |  42.3598648         8  5.29498311   Prob > F        =    0.0008
    Residual |  441.764296       289  1.52859618   R-squared       =    0.0875
-------------+----------------------------------   Adj R-squared   =    0.0622
       Total |  484.124161       297  1.63004768   Root MSE        =    1.2364

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
lottery_treat~t |  -.3987542     .16863    -2.36   0.019    -.7306528   -.0668556
        minutes |   .0109165   .0071029     1.54   0.125    -.0030635    .0248964
      education |   .0905917   .0574108     1.58   0.116    -.0224045     .203588
            age |   .0114257   .0058875     1.94   0.053     -.000162    .0230135
         income |   .0812899   .0532918     1.53   0.128    -.0235995    .1861792
politicalinte~t |    .000632   .1407503     0.00   0.996    -.2763937    .2776576
newsconsumption |   .0837987   .1372225     0.61   0.542    -.1862835    .3538809
           vote |  -.0269895   .0401661    -0.67   0.502    -.1060446    .0520656
          _cons |   3.423297   .6751106     5.07   0.000      2.09454    4.752054
---------------------------------------------------------------------------------
The number of observations in the data is less than the number of simulations. Exp
> anding the data to the number of simulations
----------------------------------------------------------------------------------
> --
        Effect                 |  Mean           [95% Conf. Interval]
-------------------------------+--------------------------------------------------
> --
        ACME                   | -.0388769     -.1061129      .0068287
        Direct Effect          | -.3957516     -.7385711     -.0637404
        Total Effect           | -.4346285     -.7789309     -.1018579
        % of Tot Eff mediated  |  .0886364      .0484105      .3322434
----------------------------------------------------------------------------------
> --

. 
. 
. /*****************************************************
> Figure A18. Average Causal Mediation Effect of the Bonus Treatment on the Number
>  of Correct Predictions as a Function Degree of Violation of Sequential Ignorabi
> lity Assumption.
> ******************************************************/
. 
. medsens (regress minutes bonus_treatment education age income politicalinterest 
> newsconsumption vote) (regress p_correct bonus_treatment minutes education age i
> ncome politicalinterest newsconsumption vote), treat(bonus_treatment) mediate(mi
> nutes) sims(1000)
Dropping existing variable _med_rho
Dropping existing variable _med_delta0
Dropping existing variable _med_updelta0
Dropping existing variable _med_lodelta0
Dropping existing variable _med_delta1
Dropping existing variable _med_updelta1
Dropping existing variable _med_lodelta1

      Source |       SS           df       MS      Number of obs   =       298
-------------+----------------------------------   F(7, 290)       =      3.47
       Model |  2533.13109         7   361.87587   Prob > F        =    0.0014
    Residual |  30207.9445       290  104.165326   R-squared       =    0.0774
-------------+----------------------------------   Adj R-squared   =    0.0551
       Total |  32741.0756       297  110.239312   Root MSE        =    10.206

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
bonus_treatment |   3.669973   1.369607     2.68   0.008     .9743439    6.365603
      education |  -.4407015   .4756744    -0.93   0.355    -1.376913    .4955104
            age |   .0513838   .0483968     1.06   0.289    -.0438697    .1466372
         income |  -1.247928   .4328745    -2.88   0.004    -2.099902   -.3959543
politicalinte~t |   1.584478   1.159677     1.37   0.173    -.6979729     3.86693
newsconsumption |  -1.092546   1.130865    -0.97   0.335    -3.318289    1.133197
           vote |  -.3584156   .3309038    -1.08   0.280    -1.009693     .292862
          _cons |   23.56129   5.352416     4.40   0.000     13.02678     34.0958
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       298
-------------+----------------------------------   F(8, 289)       =      2.72
       Model |  33.9113787         8  4.23892234   Prob > F        =    0.0066
    Residual |  450.212782       289   1.5578297   R-squared       =    0.0700
-------------+----------------------------------   Adj R-squared   =    0.0443
       Total |  484.124161       297  1.63004768   Root MSE        =    1.2481

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        minutes |   .0136451   .0071812     1.90   0.058     -.000489    .0277793
bonus_treatment |  -.0427229   .1695529    -0.25   0.801     -.376438    .2909921
      education |   .0948597   .0582573     1.63   0.105    -.0198026     .209522
            age |   .0126213     .00593     2.13   0.034     .0009498    .0242929
         income |   .0893651   .0536903     1.66   0.097    -.0163086    .1950387
politicalinte~t |  -.0075844   .1422751    -0.05   0.958    -.2876112    .2724424
newsconsumption |   .0886426   .1385182     0.64   0.523    -.1839898     .361275
           vote |  -.0270167   .0405487    -0.67   0.506    -.1068249    .0527915
          _cons |    3.18027   .6760731     4.70   0.000     1.849619    4.510922
---------------------------------------------------------------------------------
file /var/folders/3r/sktq2lwj3fl3k94lykyp8wm80000gn/T//S_45066.000002 saved


----------------------------------------------------------------
Sensitivity results
----------------------------------------------------------------
        Rho at which ACME = 0            |     .1111
        R^2_M*R^2_Y* at which ACME = 0:  |     .0123
        R^2_M~R^2_Y~ at which ACME = 0:  |     .0106
----------------------------------------------------------------
95% Confidence interval

. twoway rarea _med_updelta0 _med_lodelta0 _med_rho, bcolor(gs14) || line _med_del
> ta0 _med_rho , lcolor(black) graphregion(color(white)) mcolor(black) ytitle("ACM
> E") xtitle("Sensitivity parameter: {&rho}") legend(off) title("ACME({&rho})")

. 
. 
. /*****************************************************
> Figure A19. Average Causal Mediation Effect of the Random Bonus Treatment on the
>  Number of Correct Predictions as a Function Degree of Violation of Sequential I
> gnorability Assumption.
> ******************************************************/
. 
. medsens (regress minutes random_bonus_treatment education age income politicalin
> terest newsconsumption vote) (regress p_correct random_bonus_treatment minutes e
> ducation age income politicalinterest newsconsumption vote), treat(random_bonus_
> treatment) mediate(minutes) sims(1000)
Dropping existing variable _med_rho
Dropping existing variable _med_delta0
Dropping existing variable _med_updelta0
Dropping existing variable _med_lodelta0
Dropping existing variable _med_delta1
Dropping existing variable _med_updelta1
Dropping existing variable _med_lodelta1

      Source |       SS           df       MS      Number of obs   =       298
-------------+----------------------------------   F(7, 290)       =      3.05
       Model |  2245.22313         7  320.746161   Prob > F        =    0.0041
    Residual |  30495.8524       290  105.158112   R-squared       =    0.0686
-------------+----------------------------------   Adj R-squared   =    0.0461
       Total |  32741.0756       297  110.239312   Root MSE        =    10.255

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
random_bonus_~t |    2.93214   1.401909     2.09   0.037     .1729343    5.691346
      education |  -.3582925    .476107    -0.75   0.452    -1.295356    .5787709
            age |    .031843   .0489138     0.65   0.516     -.064428    .1281141
         income |  -1.273576   .4348218    -2.93   0.004    -2.129383   -.4177697
politicalinte~t |   2.151009    1.17329     1.83   0.068    -.1582343    4.460252
newsconsumption |  -1.262837    1.13899    -1.11   0.268    -3.504571    .9788973
           vote |  -.3548892   .3324965    -1.07   0.287    -1.009301    .2995231
          _cons |    22.7902   5.376619     4.24   0.000     12.20806    33.37234
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       298
-------------+----------------------------------   F(8, 289)       =      3.06
       Model |  37.7838323         8  4.72297904   Prob > F        =    0.0025
    Residual |  446.340329       289   1.5444302   R-squared       =    0.0780
-------------+----------------------------------   Adj R-squared   =    0.0525
       Total |  484.124161       297  1.63004768   Root MSE        =    1.2428

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        minutes |   .0119727   .0071165     1.68   0.094    -.0020339    .0259794
random_bonus_~t |   .2744854   .1711724     1.60   0.110    -.0624172    .6113879
      education |   .0891337   .0577552     1.54   0.124    -.0245405    .2028078
            age |   .0116176   .0059321     1.96   0.051    -.0000581    .0232933
         income |   .0875878   .0534693     1.64   0.102    -.0176508    .1928264
politicalinte~t |   .0245074   .1430113     0.17   0.864    -.2569683    .3059831
newsconsumption |    .071376   .1383251     0.52   0.606    -.2008764    .3436284
           vote |  -.0267729   .0403739    -0.66   0.508    -.1062371    .0526914
          _cons |   3.197342   .6714678     4.76   0.000     1.875755    4.518929
---------------------------------------------------------------------------------
file /var/folders/3r/sktq2lwj3fl3k94lykyp8wm80000gn/T//S_45066.000002 saved


----------------------------------------------------------------
Sensitivity results
----------------------------------------------------------------
        Rho at which ACME = 0            |     .0985
        R^2_M*R^2_Y* at which ACME = 0:  |     .0097
        R^2_M~R^2_Y~ at which ACME = 0:  |     .0083
----------------------------------------------------------------
95% Confidence interval

. twoway rarea _med_updelta0 _med_lodelta0 _med_rho, bcolor(gs14) || line _med_del
> ta0 _med_rho , lcolor(black) graphregion(color(white)) mcolor(black) ytitle("ACM
> E") xtitle("Sensitivity parameter: {&rho}") legend(off) title("ACME({&rho})")

. 
. 
. /*****************************************************
> Figure A20. Average Causal Mediation Effect of the Lottery Treatment on the Numb
> er of Correct Predictions as a Function Degree of Violation of Sequential Ignora
> bility Assumption.
> ******************************************************/
. 
. medsens (regress minutes lottery_treatment education age income politicalinteres
> t newsconsumption vote) (regress p_correct lottery_treatment minutes education a
> ge income politicalinterest newsconsumption vote), treat(lottery_treatment) medi
> ate(minutes) sims(1000)
Dropping existing variable _med_rho
Dropping existing variable _med_delta0
Dropping existing variable _med_updelta0
Dropping existing variable _med_lodelta0
Dropping existing variable _med_delta1
Dropping existing variable _med_updelta1
Dropping existing variable _med_lodelta1

      Source |       SS           df       MS      Number of obs   =       298
-------------+----------------------------------   F(7, 290)       =      3.34
       Model |   2442.4601         7  348.922872   Prob > F        =    0.0019
    Residual |  30298.6155       290  104.477984   R-squared       =    0.0746
-------------+----------------------------------   Adj R-squared   =    0.0523
       Total |  32741.0756       297  110.239312   Root MSE        =    10.221

---------------------------------------------------------------------------------
        minutes |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
lottery_treat~t |   -3.45935   1.379243    -2.51   0.013    -6.173945   -.7447551
      education |  -.3351698   .4742264    -0.71   0.480    -1.268532    .5981923
            age |    .032103   .0486373     0.66   0.510    -.0636239    .1278299
         income |  -1.316636    .433745    -3.04   0.003    -2.170324    -.462949
politicalinte~t |   1.863629   1.158474     1.61   0.109    -.4164531    4.143711
newsconsumption |  -1.113926   1.132578    -0.98   0.326    -3.343041     1.11519
           vote |  -.3550324   .3314115    -1.07   0.285    -1.007309    .2972445
          _cons |    24.5934   5.391296     4.56   0.000     13.98238    35.20443
---------------------------------------------------------------------------------

      Source |       SS           df       MS      Number of obs   =       298
-------------+----------------------------------   F(8, 289)       =      3.46
       Model |  42.3598648         8  5.29498311   Prob > F        =    0.0008
    Residual |  441.764296       289  1.52859618   R-squared       =    0.0875
-------------+----------------------------------   Adj R-squared   =    0.0622
       Total |  484.124161       297  1.63004768   Root MSE        =    1.2364

---------------------------------------------------------------------------------
      p_correct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        minutes |   .0109165   .0071029     1.54   0.125    -.0030635    .0248964
lottery_treat~t |  -.3987542     .16863    -2.36   0.019    -.7306528   -.0668556
      education |   .0905917   .0574108     1.58   0.116    -.0224045     .203588
            age |   .0114257   .0058875     1.94   0.053     -.000162    .0230135
         income |   .0812899   .0532918     1.53   0.128    -.0235995    .1861792
politicalinte~t |    .000632   .1407503     0.00   0.996    -.2763937    .2776576
newsconsumption |   .0837987   .1372225     0.61   0.542    -.1862835    .3538809
           vote |  -.0269895   .0401661    -0.67   0.502    -.1060446    .0520656
          _cons |   3.423297   .6751106     5.07   0.000      2.09454    4.752054
---------------------------------------------------------------------------------
file /var/folders/3r/sktq2lwj3fl3k94lykyp8wm80000gn/T//S_45066.000002 saved


----------------------------------------------------------------
Sensitivity results
----------------------------------------------------------------
        Rho at which ACME = 0            |       .09
        R^2_M*R^2_Y* at which ACME = 0:  |     .0081
        R^2_M~R^2_Y~ at which ACME = 0:  |     .0068
----------------------------------------------------------------
95% Confidence interval

. twoway rarea _med_updelta0 _med_lodelta0 _med_rho, bcolor(gs14) || line _med_del
> ta0 _med_rho , lcolor(black) graphregion(color(white)) mcolor(black) ytitle("ACM
> E") xtitle("Sensitivity parameter: {&rho}") legend(off) title("ACME({&rho})")

. 
. 
. save "pilot.dta", replace
file pilot.dta saved

. 
. log close
      name:  <unnamed>
       log:  /Users/thomasjamieson/Dropbox/Academic/Working Papers/Information and
>  Predictions/JEPS_replication.log
  log type:  text
 closed on:  14 Jun 2019, 11:57:06
----------------------------------------------------------------------------------
